Systems and methods with identity verification by comparison and interpretation of skin patterns such as fingerprints

ABSTRACT

Preferably a sensor receives a print image from an authorized person to form a template, and from a candidate to form test data. Noise variance is estimated from the test data as a function of position in the image, and used to weight the importance of comparison with the template at each position. Test data are multilevel, and are bandpassed and normalized--and expressed as local sinusoids--for comparison. A ridge spacing and direction map of the template is stored as vector wavenumber fields, which are later used to refine comparison. Global dilation--and also differential distortions--of the test image are estimated, and taken into account in the comparison. Comparison yields a test statistic that is the ratio, or log of the ratio, of the likelihoods of obtaining the test image assuming that it respectively was, and was not, formed by an authorized user. The test statistic is compared with a threshold value, preselected for a desired level of certainty, to make the verification decision--which controls access to a utilization system such as facilities, equipment, a financial service, or a system for providing or receiving information. Certain forms of the invention also encompass the utilization system. Nonvolatile memory holds instructions for automatic operation as described above.

RELATED U. S. PATENT APPLICATIONS

Two coowned, copending applications are related: Ser. No. 08/382,220 ofJ. Kent Bowker and Stephen C. Lubard, Ph. D., filed Jan. 31, 1995, andissued Sep. 22, 1998, U.S. Pat. No. 5,812,252; and attorney docketxAA-15, filed generally concurrently herewith on Sep. 9, 1996, of J.Kent Bowker et al., and entitled "ECONOMICAL SKIN-PATTERN-ACQUISITIONAPPARATUS FOR ACCESS CONTROL; SYSTEMS CONTROLLED THEREBY", later madeSer. No. 08/709,785, status pending. Both applications are whollyincorporated by reference into the present document.

FIELD OF THE INVENTION

This invention relates generally to systems and methods for verifyingidentity of people, by comparison and interpretation of skin patternssuch as fingerprints; and more particularly to novel firmware andsoftware stored in apparatus memories, as portions of apparatus, forinterpreting such patterns and controlling utilization devices. Withrespect to certain of the appended claims, the invention further relatesto systems that include such utilization devices.

A utilization device is, for example, a facility, apparatus, means forproviding a financial service, or means for providing information. Thephrase "utilization device" thus encompasses, but is not limited to,businesses, homes, vehicles, automatic teller machines,time-and-attendance systems, database-searching services, and a greatmany other practical systems. An apparatus memory for such storage is,for example, a programmable read-only memory ("PROM"), or acomputer-readable disc.

BACKGROUND OF THE INVENTION

Classical methods for evaluation of fingerprints. toeprints, palmprintsand like skin patterns entail location, categorization and tabulation ofminutiae. Efforts to adapt these classical techniques for automatedprint verification have received great attention and elaboration, butare fundamentally limited by their sensitivity to measurement noise atthe location of the miniutiae.

Automated analysis based on minutiae also is inherently very dependenton image enhancement--which often breaks down when initial data qualityis marginal. For these reasons some workers have explored othermethodologies.

Some seemingly promising efforts employ holograms--either directthree-dimensional images of prints, or holographic Fourier transforms(which have the advantage of being position invariant). Some of thesetechniques, for best results, impose costly demands on special memorydevices for storing the holograms. These holographic correlators are inessence modern refinements of much earlier two-dimensionaldirect-optical-overlay correlators such as that described by Green andHalasz in U.S. Pat. No. 3,928,842.

An intermediate ground is represented by a few relatively sophisticatedpatents that use digital computers to (1) automatically select one ormore distinctive small regions--not necessarily minutiae--in a masterprint or "template", and then (2) automatically look for one or more ofthese selected small regions in a print provided by a person whopurports to be the maker of the template. These earlier patentsparticularly include U.S. Pat. Nos. 5,067,162 of Driscoll, 5,040,223 ofKamiya, 4,982,439 of Castelaz, 4,805,223 of Denyer, and 4,803,734 ofOnishi.

All of these latter patents describe making final verification decisionsbased upon such comparisons of small regions. In this they areunavoidably flawed in their excessive dependence upon isolated, smallamounts of data--more specifically, very small fractions of theavailable information in a candidate user's print.

Some of the patents in the above list do describe sound techniques forone or another part of their respective processes. Some workers, such asDriscoll and Kamiya, use correlation methods (but electronic-datacorrelation methods, not optical correlation methods) to choose thesmall reference sections in the enrollment process--i. e., in formingthe template--and also in comparison of those regions with features in acandidate user's print. Denyer similarly uses an approximation to suchcorrelation technique.

These patents do generally allow for the possibility that the authorizeduser's template may be shifted, or in other words translated, inplacement of the print image on the sensor. Some (particularly Driscolland Denyer) allow for the possibility that the template may be rotatedtoo.

Driscoll discusses finding a least-squares-fit between plural referenceregions and a potentially corresponding plurality of test regions in thecandidate print. He suggests that departures from an ideal rotatedpattern of the reference regions is to be accounted for by distortion ofthe fingertip in the course of placement on a sensor, but by hisleast-squares approach also suggests that such distortion is inherently"random" in the sense of lacking internal correlation. whereasdistortions of flesh-and-skin structures are in fact random in the senseof being modeled or modelable statistically, proper efforts at suchmodeling must take into account that neighboring portions of thestructure exert influences upon one another, resulting in physicalcorrelations. In short, neighbors are softly constrained.

Driscoll's approach, in using a least-squares fit--to accommodatedepartures from a rigid rotation that underlies the distortion--inessence disregards such correlations; at best, he only considers a smallpart of the operative statistics. Denyer, too, briefly mentions (thoughin a much more generalized and tangential way) the possibility ofsomehow accounting for distortion.

All of these patents, however, fail to take account of dilations (or, toput it more completely, dilations or contractions) which an authorizeduser's fingertip may undergo--relative to the same user's establishedtemplate. Such dilations may arise from variations in the pressure withwhich the finger is applied to an optical or other sensor (capacitive,variable-resistance etc.).

Such dilations may be expected to have at least a component which isinvariant across the entire image, in other words a dilation withoutchange of fingerprint shape--an isomorphic dilation. Furthermore all theabove-mentioned patents fail to make systematic, controlled allowancefor dilations and other forms of distortion that are differential--whichis to say, nonisomorphic.

Correlation methods, matched-filter methods, and (loosely speaking)related overlay-style techniques of comparison all fail totally in anyarea where a reference print is mismatched to a candidate print by aslittle as a quarter of the spacing between ridges. I have found thatdilations and other distortions can and commonly do produce spuriousmismatches locally--over sizable areas--exceeding twice the spacingbetween ridges, that is, many times the minimum disruption whichdestroys correlation and thereby recognition.

Therefore, failure to account properly for either dilation (isomorphicdistortion) or distortion differential distortion) results inunacceptably high rates of failure to verify or recognize an authorizeduser--i. e., high rates of the so-called "false rejection" or "type 1error". Artificial measures aimed at reducing this failure rate leadinevitably to the converse: unacceptably high rates of failure to rejectunauthorized users, impostors--i. e., high rates of the so-called "falseacceptance" or "type 2 error".

Merely allowing for some distortion, in a statistically uncontrolledway, can never cure this fundamental failing. Skin and flesh distortiondoes not affect prints in an uncorrelated way, but rather in partiallysystematic ways that arise from the physical character of skin andflesh. I believe that failure to account properly for distortion is thesingle greatest contributor to poor performance of fingerprint verifyingsystems heretofore.

Furthermore variations in habits of placement of a fingertip on a sensortend to be somewhat systematic. These systematic properties of theprint-forming process have their own statistically characteristicpatterns--their own statistics.

In the context of any given comparison method, these special statisticsexert particular characteristic effects on the results. All the patentsmentioned above appear to ignore these statistics, in the processdiscarding very important information that bears strongly onverification decisions.

In addition, the patents listed above fail to make use of modernprinciples of decision theory and signal processing that have been usedto great advantage in other fields. Driscoll, for instance, whilediscussing the final stages of his analysis in terms reminiscent of theestablished Neyman-Pierson analysis, does not appear to properly applythe principles of that analysis. Such principles have been importantlyapplied in industrial, military, and scientific pattern-recognitionproblems, but workers in the practical fingerprint field do not appearto be aware of these principles or in any event are not evidently usingthem.

Similarly none of the patents noted makes use of decisionaldownweighting of data from areas that are less certain or noisier;rather, to the extent that any consideration at all is given to suchmatters, noisy data are simply discarded--a very undesirable way totreat expensive data. Bandpassing of test data is not seen in thesereferences, although certain other forms of filtering are used byDriscoll and others. Normalizing is likewise absent--except for trivialforms implicit in binarization or trinarization, used in many printanalyzers. None of the noted patents teaches expression of test andtemplate data, or comparison of such data with one another, in terms oflocal sinusoids.

Thus the skin-pattern verification field has failed to make good use ofall available data, take effective account of dilations or distortions,make suitable allowance for known statistics of placement variation, andapply modern decisional and signal-processing tools. As can now be seen,the prior art in this field remains subject to significant problems, andthe efforts outlined above--although praiseworthy--have left room forconsiderable improvement.

SUMMARY OF THE DISCLOSURE

The present invention introduces such improvement, and performsfingerprint verifications with an outstandingly high accuracy notavailable heretofore. The invention has several facets or aspects whichare usable independently--although for greatest enjoyment of theirbenefits I prefer to use them together, and although they do haveseveral elements in common. The common parts will be described first.

In its preferred apparatus embodiments, the present invention isapparatus for verifying the identity of a person. It operates bycomparing (1) test data representing a two-dimensional test image ofthat person's skin-pattern print with (2) reference data derived from atwo-dimensional reference skin-pattern print image obtained during aprior enrollment procedure. Each of the apparatus embodiments includessome means for holding instructions for automatic operation of the otherelements of the apparatus; these instruction-holding means include ormake use of a nonvolatile memory device, and may be termed the"nonvolatile memory means".

Now in preferred embodiments of a first of its independent aspects, theapparatus includes some means for extracting from the test data anestimate of noise variance in the test data. For purposes of breadth andgenerality in expression of the invention, these means will be calledsimply the "extracting means"; they extract a noise-variance estimate asa function of position in the test image.

The apparatus of this first facet of the invention also includes somemeans for comparing portions of the test and reference data, forcorresponding positions in the two images. Once again for generality andbreadth these means will be called the "comparing means".

In addition the apparatus includes some means for weighting theimportance of comparison for each portion. These means--again the"weighting means"--weight the importance of comparison for each portionin accordance with the noise-variance estimate for the correspondingposition.

Also included are some means, responsive to the weighting means, formaking an identity-verification decision--identified here as the"decision-making means".

The foregoing may be a description or definition of the first facet oraspect of the present invention in its broadest or most general terms.Even in such general or broad form, however, as can now be seen thefirst aspect of the invention significantly contributes to resolving thepreviously outlined problems of the prior art. In particular, the use ofdown-weighting for noisier regions of a print is a major step towardenabling use of essentially all available data.

All of the apparatus forms of the invention are preferably practicedincorporating some sensor means for acquiring the test data, and somemeans, responsive to the decisionmaking means, for operating a switch.Thus the invention provides a practical real-world system, not anabstraction.

Now turning to a second of the independent facets or aspects of theinvention: in preferred embodiments of this second facet, the inventionapparatus includes some means for deriving from the test datacorresponding multilevel test data that are bandpassed and normalized.For reasons suggested earlier these means may be denoted the "derivingmeans".

For the purposes of this document the term "normalize" is to beunderstood as describing a true stretching (or compression) of thedynamic range of data to a standard range--while maintaining multilevelcharacter of the data. This normalization thus is understood to bebeyond the trivial forms seen in prior-art binarization andtrinarization, which force all data to be only binary or at mosttrinary.

This apparatus also has comparing means related to those described abovefor the first aspect--but here the comparing means are for comparingportions of the bandpassed and normalized multilevel test data with thereference data. In addition it has decision-making means, also relatedto those described earlier--but here the decision-making means areresponsive to the comparing means.

The foregoing may constitute a definition or description of the secondfacet or aspect of the present invention in its broadest or most generalterms. Even in such general or broad form, however, as can now be seenthe second aspect of the invention resolves the previously outlinedproblems of the prior art.

In particular such an apparatus by taking advantage of signal-enhancingtechniques of bandpassing and normalization the invention improves bothactual signal-to-noise relations and effective signal-to-noise relationsin the system, in terms of best use of the available data-handlingcapability.

These advantages have not heretofore been enjoyed by skin-patternverification systems. In this way this second facet of the invention tooleads toward greater precision and accuracy in verifying prints.

In a third of its independent facets, the invention apparatus includesmeans for expressing the test data in the form of local sinusoids, andmeans for expressing the reference data in the form of local sinusoids.The apparatus also includes comparing means--but here the comparingmeans compare portions of the sinusoidally expressed test data with thesinusoidally expressed reference data.

Decision-making means are also included, responsive to the comparingmeans as just defined. By operating on the data in sinusoidal form theinvention in preferred embodiments of this third aspect is able toexploit many advanced signal-processing techniques, particularlyincluding the Fast Fourier Transform (FFT), multiplicative operations inthe frequency domain in lieu of convolutions in the spatial domain,back-transformations to find spatial results etc.--each of which saves agreat amount of computational time and effort without loss of accuracy.

While optical Fourier transforms have been applied in holographicfingerprint systems, as mentioned earlier, neither sinusoidalrepresentations nor Fourier treatment of digital data has heretoforebeen used in this field.

Preferred apparatus embodiments of the invention in a fourth of itsindependent facets include some means for deriving from the referencedata a map of ridge spacing and direction. These deriving means alsostore the map as one or more vector wavenumber fields.

Further included are some means for comparing portions of the test datawith the reference data; these comparing means include means for usingthe vector wavenumber fields to refine the comparing operation. Theapparatus also includes decision-making means responsive to thesecomparing means.

While some earlier systems do make one or another type of ridge map,typical earlier uses proceed to direct comparison of the maps. Nonestores the map in the form of a vector wavenumber field for later use inrefining a discrete comparing operation.

This aspect of the invention enables several extremely effective uses ofthe ridge spacing and direction data in adjustments of theauthorized-user template for fairer comparison with a candidate user'sfingerprint. Such advantages will be more clearly seen in later sectionsof this document.

Apparatus of preferred embodiments according to a fifth independentaspect or facet of the invention includes some means for estimating theassumed dilation of the test image relative to a reference image--i. e.,"dilation-estimating means". The dilation here mentioned is to beunderstood as having a global character--in other words, affecting theentire print uniformly, without change of shape. The dilation-estimatingmeans thus estimate isomorphic dilation.

The apparatus also includes means for comparing the test data with thereference data, taking into account the estimated dilation. Theapparatus also includes decision-making means that respond to thesecomparing means.

This facet of the invention too advances the art meaningfully as itenables two major operating improvements. The first of these is findingsmall regions of a candidate-user print that correspond to selecteddistinctive regions of the authorized-user template--even in thepresence of dilations that would otherwise destroy the correlation andso impair recognition.

The second major operating improvement attributable to this fifthindependent aspect of the invention is particularly efficient operationof a more-general distortion-estimating aspect of the invention thatwill be described below. My global-dilation evaluating feature gives thelater distortion estimator a running start, in that the distortionestimator need seek only the spatially differential part of the overalldistortion--perturbations, in other words, of the global, isomorphicdilation.

Apparatus according to a sixth independent aspect of the inventionincludes some means for estimating an assumed distortion of the testimage relative to a reference image. Here the distortion underdiscussion particularly includes nonisomorphic distortion.

As will be understood, however, the distortion here mentioned typicallyalso includes an isomorphic component--to the extent that previousdetection of and accounting for isomorphic dilation was imperfect, orperhaps was not provided at all. The apparatus also includes means forcomparing the test data with the reference data, taking into account theestimated distortion; and decision-making means responsive to thesecomparing means.

Although all the independent aspects and facets of my invention makeextremely important contributions to excellent performance of myinvention, the distortion-estimating means resolve the root cause ofwhat I consider the greatest single defect in prior systems. Assuggested earlier, it is this defect that especially impairs the abilityof prior systems to reliably recognize an authorized user--i. e., torecognize a clear, clean template which has simply been slightlydistorted.

In particular the estimation of distortion enables application of theestimated distortion to approximately equalize the test and referencedata with respect to the assumed distortion. The comparing means canthen compare the thus-approximately-equalized test and reference data.

This can be done particularly straightforwardly, by using the estimateddistortion to generate a matched filter for use in forming a teststatistic. In both the filter generation and the actual use of the teststatistic thereby formed, the system can readily be made to take intoaccount estimated noise variance in the test data, as a function ofposition in the test image.

The distortion adjustment underlies and enables all such refinements.The result is an overall level of excellence in recognition oftemplates, even in the presence of unusual distortions--leading in turnto truly extraordinary low error rates of both the "false rejection" and"false acceptance" types.

Details of operation of the distortion-estimating means--includingdemodulation of the test data, smoothing, downsampling and then acautiously expanding gradient search for the assumed distortion field,to avoid loss of phase registration--will all be presented below.

In a seventh of its independent facets or aspects, preferred apparatusembodiments of the invention include some means for comparing the testdata with the reference data to form a test statistic as the ratio, orlogarithm of the ratio, of the likelihoods of two contrary hypotheses:

likelihood of obtaining the test image, assuming that the candidate useris the same person who also formed the reference fingerprint image(template), and

likelihood of obtaining the test image, assuming that a different personformed the reference print image.

This apparatus also includes decision-making means responsive to thetest statistic.

This aspect of the invention thus for the first time in the fingerprintfield makes proper use of established principles of decision theory.Print verifications are thereby placed on a sound footing that actuallyleads to the most conclusive decision that can justifiably be made fromthe available information--no more, no less.

Fingerprint-based verifications of identity have long suffered from anabsence of such sound operation. Advantageously my comparison means arecombined with means for comparing the test statistic with a thresholdvalue, preselected to impose a desired level of certainty inverification.

Preferred apparatus embodiments of yet an eighth independent facet oraspect of my invention diverge somewhat from the first seven. Theapparatus here is for receiving surfacerelief data from a sensor thatacquires surface-relief data from a relieved surface such as afinger--and in response controlling access to facilities, equipment, afinancial service, or a system for providing or receiving information.

The apparatus is for use in the presence of an assumed dilation of therelieved surface. The apparatus includes a system for processing thereceived data to determine identity of the relieved surface. In additionto the previously mentioned instruction-holding memory means, thissystem includes:

means for analyzing the data to estimate the assumed dilation,

means for comparing the test data with reference data, taking intoaccount the estimated dilation, and

means, responsive to the comparing means, for making anidentity-verification decision.

In addition, the overall apparatus includes some means for applying thedetermined identity to control access to such fa3 cilities, equipment,financial service, or source or reception of information. Thus thisaspect of the invention, while spe5 cifically incorporating thedilation-estimating feature men6 tioned above in connection with thefifth independent aspect, particularly focuses on and includes, as partof the inven8 tion, components that actually control access to varioustypes of utilization means.

A ninth independent facet of the invention involves a furtherdivergence, in that it is a secured system subject to access controlbased upon surface-relief data from a relieved surface such as a finger.This system is for use in the presence of an assumed distortion of therelieved surface.

The system includes utilization means, susceptible to misuse in theabsence of a particular such relieved surface that is related to anauthorized user. The utilization means being selected from the groupconsisting of:

a facility,

apparatus,

means for providing a financial service, and

means for providing or receiving information.

In addition the system includes sensor means for acquiringsurface-relief data from such a relieved surface.

The system also includes some means for processing the data to determineidentity of the relieved surface, and for applying the determinedidentity to control access to the utilization means. These processingand applying means include, in addition to the instruction-holdingmemory means:

means for analyzing the data to estimate the assumed distortion,

means for comparing the test data with reference data related to theparticular relieved surface related to the authorized user, taking intoaccount the estimated distortion, and

means, responsive to the comparing means, for making anidentity-verification decision.

Thus this aspect of the invention includes the utilization meansthemselves, as well as the access-control intermediary that is includedin the eighth aspect of the invention.

While thus focusing on and including the utilization means, theinvention makes use of the distortion-estimating feature discussedearlier in connection with the sixth independent facet of the invention.

In a tenth of its independent aspects or facets, preferred embodimentsof the invention take the form of a method, rather than apparatus. Thismethod is for verifying the identity of a person. The method does so bycomparing test data representing a two-dimensional test image of thatperson's skin-pattern print with reference data derived from atwo-dimensional reference skin-pattern print image obtained during aprior enrollment procedure.

The method includes the step of extracting from the test data anestimate of noise variance in the test data as a function of position inthe test image. It also includes the step of comparing portions of thetest and reference data, for corresponding positions in the two images.

Furthermore the method includes the steps of weighting the importance ofcomparison for each portion, in accordance with the noise-varianceestimate for the corresponding position; and--responsive to theweighting means--making an identity-verification decision. Another stepis, in nonvolatile memory, holding instructions for automatic operationof the foregoing steps.

Thus the method partakes of the advantageousness of the noise-weightingapparatus embodiments of the first independent aspect of the invention,discussed earlier. Preferably this method is optimized by incorporationof other features or characteristics, particularly the steps ofoperating a sensor to acquire the test data and--responsive to thedecision-making step--operating a switch if identity is verified.

All of the foregoing operational principles and advantages of thepresent invention will be more fully appreciated upon consideration ofthe following detailed description, with reference to the appendeddrawings, of which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart or block diagram showing, for certain preferredembodiments of my invention, how different portions of the programmedfirmware perform the processes of the invention;

FIG. 2 is a rough conceptual presentation of a windowed subset of theauthorized-user template, arrayed with sixty-three isomorphs of thatsubset--nine rotations and seven dilations (including the original);

FIG. 3 is a rough conceptual diagram of the original subset of FIG. 2 inposition in the authorized-user template, and one of the nine-by-sevenarray of isomorphs linking that template with the candidate data;

FIG. 4 is a rough conceptual diagram, conveying the general principle ofapplying a distortion field to modify the template;

FIG. 5 is a highly enlarged conceptual diagram of a whorl area in afingerprint, particularly illustrating changes of interridge phase inthe area;

FIG. 6 is a graph or diagram showing relationships of a very generalrepresentative "test statistic";

FIG. 7 is a like view for a test statistic 52 of FIG. 1, in accordancewith the present invention; and

FIG. 8 is an overall block diagram showing the embodiment of myinvention in a hardware system.

DETAILED DESCRIPTION OF THE PREFERRED EMODIMENTS

Inputs--As FIG. 1 shows, preferred embodiments have at least threegroups of inputs: one group of inputs from the candidate user of aweapon or other apparatus, another from the authorized user (or thatperson's surrogates), and the third from generalized population data.The candidate's inputs include a fingerprint-image data array 11 and acommand 57 (at bottom left in the drawing) that the apparatus operate.The data array 11 originates from a skin-pattern detector, which is mostrepresentatively an optical sensor array but may instead be of anothertype such as capacitive, variable-resistive or high-frequency acoustic.

The authorized user's inputs include a fingerprint-image data array 21(originating analogously to the array 11 for the candidate user,discussed above), and a parameter setting 27 which reflects the desiredcertainty with which a fingerprint match must be found. The authorizeduser does not necessarily personally enter this parameter 27 into thesystem, but may instead indicate a selection of the value, or acquiescein the value, of this parameter.

The desired-certainty threshold parameter 27 is related to the relativenumbers of false positives and false negatives to be tolerated--but notin an arithmetically direct way, rather in complicated statistical waysas will be explained in further detail later in this document. For thisreason, a more precisely correct name for this threshold parameter 27might be more abstract, e. g. "decision threshold"; however, the phrase"desired-certainty threshold" may be more helpful as it is moredescriptive.

This value is selected to reflect the type of usage anticipated. Inparticular, it can be related to the probability of false negatives, sothat it could be thought of as controlling the "desired certainty" ofacceptance for the authorized user. Alternatively, the desired-certaintythreshold old can be inversely related to the probability of falsepositives, and thus thought of as controlling (but in an inverse way)the desired certainty of rejection for an unauthorized user.

For example, if the apparatus is to control access to anadvance-fee-based gymnasium, the primary objective may be merely todiscourage occasional cheaters. In this case the certainty of acceptancefor the prepaid customer or member of the gym may be set veryhigh--accepting a significant chance of letting in someone who has notpaid.

Similarly if the apparatus is a weapon to be used in the field bymilitary or police personnel, a primary objective may be to have use ofthe weapon available to the authorized user without delay and withoutquestion. In this case the certainty level may be set relativelyhigh--accepting some small chance that the weapon might be usable by anopponent who takes it from the authorized user. In this case, however,since there are significant risks associated with an opponent'sappropriation of a weapon, the authorized-user acceptance likelihoodmight not be set quite as high as in the first example above where theadverse consequences of admitting a cheater are minor.

Now in a contrary example, for control of access to a secure areacontaining documents or apparatus of utmost sensitivity, a primaryobjective may be to exclude spies. In this case the certainty level foracceptance of authorized personnel may be set distinctly low--acceptingsome significant likelihood that an authorized individual may be delayedin entry by having to repeat the verification procedure.

Similarly if the apparatus is a weapon to be kept in a home forprotection against intruders, a primary objective may be to preventunauthorized use by children or teenagers who live or visit in the home.In this case the certainty level may be set relatively low--acceptingsome small degree of unreliability in the weapon's availability for useagainst intruders--but perhaps not as low as in the immediatelypreceding example, since delayed availability of a weapon to anauthorized user in an emergency is ordinarily much more onerous thandelayed entry to a secure area.

A third type of input is a statistical set 17 preferably coming fromneither the candidate user nor the authorized user, but rather from ageneralized database representing people in general. Since these dataare ordinarily derived without reference to the particular people knownto be involved, I call these data "prior statistics" or "a prioristatistics".

The statistical data 17 are applied 18, 18" at certain points in theprocessing to take into account the known degree of variability in theway people place their fingers on a fingerprint-acquisition imagingdevice. This variability may differ depending on the position andorientation of the imaging device in relation to the user.

For example, variability in a panel-mounted imager at an automaticteller machine may be expected to have a statistical pattern that isdifferent from variability in a desktop imager in an office. Variabilityin an imager that is built into a tool (e.g., a weapon) may be expectedto be different still.

In some cases, particularly where a user typically is standing whileapplying a fingertip to a stationarily mounted imaging device, thisvariability may depend in part upon the height of the user. In any eventit is preferable to collect a different a priori data set using theactual type of imager and collection geometry for which a particularapparatus will be used.

In special cases, initial data acquisition may show that the authorizeduser's fingerprints have very unusual properties or characteristics. Insuch extraordinary cases better performance may result from using astatistical set 17 derived from input data 21 for the authorized user.

Such provisions require a lengthier procedure for enrollment orregistration of the authorized user, to establish not only this user'sfingerprint but also certain measures of the variability in this user'spresentation of the print to the apparatus. For good results,furthermore, such a procedure should be deferred until the authorizeduser has acquired some familiarity with the apparatus, whichintrinsically tends to lead toward habits of handling--and thereby notonly to reduced variability but also to particular patterns ofvariability.

Such extra effort might possibly be justified in special cases, as forinstance with a person who has an injury or a handicap that affects theposture or the attitude of the arm or hand. Another possible specialsituation perhaps may occur when a person of very unusually shortstature, or a person in a wheelchair, will be placing a fingerprint on adevice to operate an automatic teller machine where most users stand.Such special problems of stature, etc., if they prove signifi7 cant maybe best managed by assembling height-correlated and other speciallycorrelated statistics.

In general the use of a priori statistics, ideally collected from userswho have already formed habits in placing fingers on imagers, appearspreferable.

Procedural overview--A glance at the bold vertical lines 14, 22 in FIG.1 reveals that the fundamental scheme is to direct signals 12-14 fromthe candidate fingerprint image data 11, and signals 22-26 representingthe authorized user's preprocessed fingerprint image data or "template"21, to a common final comparison 51. Certain side calculations or signalpaths 15-16, 28-47 along the way facilitate and enhance the comparison.

Results 52-56 of the comparison 51 interact with signals 59 generated bythe candidate's command 57--in a manner controlled by thedesired-certainty threshold 27--to determine whether the command 57produces no perceptible action at all φ, or produces operation 56. (Theinvention encompasses including a no-function warning light or tone,rather no perceptible action, if utilization is denied 55d.) Preliminaryprocessing of the candidate's data--Processing of the candidate imagedata 11 begins with analysis 12 of the dynamic range of signals whichrepresent grooves and ridges within the image. The result includesforming a new image-data version 13, in which this dynamic range isnormalized, i. e. locally stretched or compressed to precisely match theoverall range of the later processing stages.

In addition the new version of the image is subjected to Fourieranalysis--expressing the data as spatial sinusoids--and bandpassfiltering, to eliminate inappropriate spatial frequencies in the imageversion 13. In the analysis 12, preferably spatial frequencies aretreated as "inappropriate" if they are not spatial frequencies 21' thatcould have originated from the similarly preprocessed print (template)21 of the authorized user.

Preprocessing of the authorized user's print to obtain the template willbe described shortly. In such original preprocessing, spatialfrequencies can be rejected based on a more leisurely harmonic-contentanalysis of the authorized user's print.

Closely associated with the range analysis 12 and resulting bandpassed,normalized sinusoidal data 13 is a downsampling step 13' which greatlyreduces the amount of data to be processed in all later stages of theprocedure. This step 13' is important because it can make the differencebetween a procedure that is unacceptably time consuming and a procedurethat is practical.

To be sure it is also important that the procedure be accurate. Properlycontrolled downsampling at this step, however, does not degrade overallperformance. More specifically, it is known that the data 13 arerepresented sinusoidally, and that these data cannot have majorcomponents at finer spatial frequencies than the smallest spacing oftroughs or ridges in the authorized user's print 21.

Accordingly, in downsampling 13' it suffices to preserve representativevalues at a reasonable fraction less than half of that smallestperiodicity--or for example about one third of the averace periodicity.Once again the template frequency content 21' is useful, in guidingselection of an optimum spatial frequency for use in the downsamplingstep 13'.

Philosophical overview--Four important characteristics of the inventioncan be gleaned already from the foregoing discussion of blocks 12through 13' in FIG. 1. First, the assumption is made throughout that thecandidate user is the authorized user--and that this assumption can beconfirmed, if only we conduct a fair comparison.

It might be supposed that this assumption will lead to an overwhelmingnumber of false-positive test results. Such a supposition would beincorrect, for I have found that a fair comparison will only highlightthe underlying differences in information content between anunauthorized candidate (impostor) and the true authorized user.

The present detailed description, as it unfolds, will make progressivelymore apparent that each intermediate process step 23-47 of myinvention--when practiced upon a typical impostor's print--is mostlikely to lead to catastrophic misalignment of the two prints. By farthe most likely end result, in the final decision 54, is a decisivedenial 55d.

The assumption under discussion is also confirmed from the oppositeperspective: what happens if the candidate user is in fact theauthorized user? A fair comparison is absolutely essential toeliminating the effects of enormous variation in fingerprint appearancedue to details of operating conditions. Such details include, inparticular, the physical and emotional condition of the user--and theseconsiderations are especially important to avoid rejecting theauthorized user.

Thus the assumption that the candidate is the authorized user only leadsto a very great reduction in the amount of data to be processed, and avery great increase in reliability of the results.

A second characteristic of the invention is an overriding plan to formrespective versions of the two data sets 11 and 21 which are adjusted tobe as much alike as possible. This adjustment, however, is only withrespect to certain data properties that are known to be variable withinmultiple trials or instances of essentially any single user to form aprint.

These particular variable data properties, within their known degree ofvariability, are at best immaterial (and at worst misleading) toidentification or verification. The invention is accordingly fashionedto ferret them out, so that they can be canceled out--in a word, toignore them.

In doing so, it is necessary to accommodate the extreme time pressureassociated with the candidate-data processing. Conversely, relativelylong times can be devoted to obtaining several instances of anauthorized user's print--and selecing the most representative one(s) ofthem, and performing image enhancement on the best instances.

It is desirable to take advantage of the available time to perform suchextra steps, though it only very occasionally turns out to have beennecessary. (In very extraordinary cases, as mentioned above inconnection with establishing the statistical set 17, in lieu of a prioristatistics, effort and time can also be devoted to determining thestatistics of variation among those instances.)

The shaded lines 58 enclose those portions of the data collection andprocessing that can be performed in advance, before deploying theapparatus or receiving the candidate user's command. These portionsinclude establishment of a statistical set 17 and the desired-certaintythreshold 27, as well as the authorized-user data collection andprocessing 21 through 22", and 28 through 31'.

A third characteristic of the invention is closely related to the firsttwo. This characteristic is that the invention makes the template asclean and as definite as possible--and then exploits that fact byprimarily relying upon the template, rather than upon the candidatedata, wherever feasible.

A first example of this is in the preferred use of the template toprovide periodicity criteria 21' for both the analysis 12 anddownsampling 13'--rather than relying upon statistics of the candidatedata 11 for the bandpassing criteria. This strategy is preferred eventhough the analysis 12 does in fact extract those candidate-datastatistics 15 for other purposes.

Later examples of this characteristic of the invention will be seenshortly in the preprocessing selection 31 and premassaging of numerouslocal subsets 31' of the template 21. This characteristic will be seenalso in the preprocessing preparation 28 of local ridge-spacing maps andvector wavenumber fields 29; and also highly specialized gradient 22'and quadrature forms 22" derived from the template 21 and wavenumberfields 29.

A fourth characteristic of the invention is that it operates on the datain terms of local sine-wave patterns, rather than as isolated binarydata bits or linear (ridge and groove) structures. Thus the initialnoise and range analysis 12 operates not only in positional space butalso in Fourier space (in other words, in terms of the spatialfrequencies in the candidate image), and the new version or filteredinformation 13 is presented as amplitudes of sinusoids associated witheach region of the original image.

By virtue of this characteristic, while guided by detection theory theinvention can also take advantage of the high computational efficiencyand fidelity of the Fast Fourier Transform (FFT). The FFT performs alarge fraction of the computationally intensive processes in thealgorithm.

Preprocessing of the authorized user's fingerprint images

During preprocessing 58 the authorized user provides a fingerprint thatwill be refined to form a template 21. Details of the refinement will bediscussed shortly.

Where time permits, best results are obtained by acquiring severalrealizations, or successive trial images, of the authorized user'sprint--and analyzing them to determine which is most representative andwhether they have any extraordinary character that may require specialhandling. This information is very useful in controlling the applicationof these data in the real-time processes that follow.

In some cases a user may appear to have more than one family or group ofrealizations--perhaps due to divergent, separate habits of gripping orpresenting a finger. In such cases it is possible to assemble acomposite of partial information from each of plural realizations, oreven to store plural entire templates (with associated respectivelikelihoods of occurrence) to be tried alternatively in evaluating acandidate print 11, 13.

In any event, from the representative authorized-user print image orimages 21, during preprocessing 58 the system selects 31 severaldistinctive regions, subsets or windows 31'. These small, preferablycircular regions 31' are stored separately from the full template 21--asare (preferably for certain embodiments) numerous versions or variantsof each region, prepared by applying a variety of crosscombinations ofvarious-sized rotations and dilations.

Since this part of the procedure is performed during preprocessing 58rather than later during decision-making time, there is a great deal offreedom to calculate the rotations and dilations by any of variousprocedures--such as, for example, by oversampling and interpolation. Forreasons that will appear shortly, however, the regions/variants 31' arepreferably stored in the form of Fourier transforms, rather thandirectly as spatial data.

Nevertheless it is preferable to calculate these transformsexpeditiously. Preferably the procedure known as a "Fast FourierTransform" (FFT) is used, although this precludes a single-steptransformation in two dimensions. Two one-dimensional FFTs can becalculated more quickly.

Other important data 21', 29, 22', 22" are also advantageously extractedfrom the template 21 during preprocessing, making best use of the moreleisurely time frame available for this work. Already mentioned are thestatistics 21' for use in the image noise and range analysis 12 of thecandidate image 11.

This information is found through data conditioning akin to that 12which is discussed elsewhere in this document in relation to thecandidate data. Also found through such data conditioning arenormalized, bandpassed data, and vector gradient fields 22' somewhatclosely related to the template data 22).

In addition, a so-called "matrix covariance estimator" is used to map 28magnitude and direction of local ridge spacings in the template 21--toform vector wavenumber fields 29, which will be used later in formingthe final template 26 for comparison 51 with the candidate data 14.During preprocessing 58 these fields 29 also are combined (not shown)with the input template data 21 in such a way as to provide smoothingalong ridge lines, in the output template data 22; and moreover are alsomultiplied by the template gradient 22' to form two quadrature-phaseforms 22" of the template data 22.

These quadrature forms 22" too will be used in forming the finaltemplate 26 for comparison--and also particularly in beginning 42 toisolate differential distortion 45 in the candidate print. Duringreal-time processing, as shown, the two quadrature forms 22" and thewavenumber fields 29 will all be modified twice 23, 25--keeping them instep 24', 29', 26', 29" with the modified direct template data 24.

In addition, flags are set up in certain of the vector wavenumber fields29 to warn of phase reversals in the template data 22, as will beexplained below. These warning flags are used in selecting one or theother of the quadrature phase forms 22", 24', 26' of the template foruse. This enables the system to avoid errors that would otherwise arisein allowing the processing to continuously traverse phasediscontinuities.

Further specifics of these preprocessing steps will be introduced belowin discussion of the processing stages that make use of these specialpreprocessed data.

Using candidate-data variance estimates--The previously discussedinitial noise analysis 12 in the candidate-data (left) half of FIG. 1may be considered roughly as a data colander, which separates data fromnoise. Both the data and the noise are then suitably directed,respectively, for beneficial use.

FIG. 1 shows that the data and the noise actually proceed to many of thesame later stages of the algorithm, in the sense that the laterprocessing blocks 34, 44, 51 receive both data and noise. In each of thelater processing modules, however, these different pieces of informationare separately received and very differently used.

Thus one of the above-mentioned side-calculation paths is application ofthe noise information 15 abstracted from the candidate data to enhancelater stages of processing. This information 15 is in the form of anarray or field of variance estimates, in effect overlaid on the reformedimage data 13 themselves.

In other words the system constructs and keeps a separate index 15 ofthe reliability of the image data 13 in each region of the image,respectively. These reliability indices are used to weight therespective significance that is attributed to each comparison or othercalculation based upon data in the corresponding image regions.

Thus for instance the noise variance array 15 is applied 16 to the finalcomparison step 51, so that the final test statistic (measure ofprobable identity between candidate and authorized user) 52 depends moreheavily on portions of the candidate data 11 that are relativelycleaner. The test is thus made to depend more lightly on portions thatare relatively noisier.

Such use of downweighted information, where the information is of lesserreliability, is far superior--in making maximum use of availableinformation--to merely setting an arbitrary criterion of reliability andthen discarding questionable information. The latter technique appears,for example, in Driscoll's selection of a very small number of"best-match" regions, and then proceeding directly to final decisionbased on such regions.

For any given intensity of calculation, and any given noisiness anddistribution of noisiness in the candidate data, the downweightingmaximizes the reliability of the results at each point in theprocedure--and overall. For like reasons the noise array 15 is alsoapplied 16', 16" to control certain others of the previously mentionedside calculations.

Global search and isomorphic adjustment: purpose--Another sidecalculation 31-38 provides a measure of simple (shape-invariant)geometrical mismatches in the formation, or realization, of thecandidate print image 11, relative to the template 21. By the terms"formation" and "realization" I mean to distinguish variations inplacement of a fingerprint from the information content of the candidateprint itself.

Preferably for certain embodiments this second side calculation 31-38,like the first, is partially performed in preprocessing time 58. Thisside calculation 31-38 accounts for displacements or translations of theentire image, rotations of the entire image, and also dilations orcontractions of the entire image resulting from variation in pressurewith which the entire fingertip is pressed against the sensor. As willbe understood, when increased pressure squashes the whole surface of thefingertip against the receiving surface, the whole fingertip surface mayexpand slightly--but preserving the original shape, i. e.isomorphically.

Of course the authorized user's initial print is taken with some appliedpressure, so each candidate-print realization may be made with eithermore or less pressure than applied in making that initial print. Hencethe amount of size change if characterized as "dilation" may be eitherpositive or negative--or, if multiplicative, as a factor greater or lessthan unity.

The global search is "global" in two senses: first, the entire candidateprint is canvassed to find one or more regions that most closely matchcertain preidentified portions of the template. Second, once the one ormore best-match regions are found the remaining mismatch is treated as apositional/dilational error with respect to the entire useful area ofboth prints.

Identifying comparison regions for the global search--The comparisonregions 31, also called "local subsets" of the template 21, are firstidentified 31 (and if desired their data separately stored) duringpreprocessing 58. They are identified 31 as regions that have someparticularly distinctive character.

Such distinctiveness may be defined for example in terms of high ratesof change of harmonic content. If preferred, within the scope of myinvention they may instead be defined in more conventional ways--such asclosely adjacent plural/multiple ridge or groove endings.

In the preferred embodiment, the choice of subset is made by locating acircular subset window in such a way as to minimize the values of thecrosscorrelation function of the windowed subset versus the entiretemplate image--at nonvanishing offset values. Preferably plural windowsare established 31 in this way, each under the assumption that anyalready-established windowed region is unavailable.

In any event it is important that the selected windows containessentially the most distinctive features of the authorized user'sprint, since they will be used to guide the process of adjusting thetemplate to match the candidate. If the features used were insteadrelatively common, the system would be more likely to perform theadjustment incorrectly even if the candidate is the authorizeduser--resulting in a false-negative finding 55d.

Each of the local subsets selected 31 represents a view of a small partof the template, as seen through a small window. The size of the windowis important: it must be large enough to contain a moderately complexand therefore truly distinctive set of features.

Nevertheless, it must be small enough to preserve correlation--which isto say, enable recognition--of its distinctive features when allowanceis made for isomorphic translations, rotations and dilations, and evenif the fingerprint has undergone more general locally-varyingdistortions.

It is also desirable that the several identified 31 subsets bereasonably well separated from each other. If they are too closetogether, they may not be independent enough to complement each other inthe ways to be described.

As suggested earlier, if a particular authorized user is found to havemore than one discrete way of placing a finger on the apparatus thenspecial provision may be made for accommodating this idiosyncrasy. (Thiscase is to be distinguished from the normal range of positioningvariation about a single mode of placement.) For instance it is possibleto incorporate auxiliary memory, perhaps at added cost, to cover theextra storage requirements--for such an authorized user who has two ormore fingerprint personalities.

Alternatively, and particularly if the authorized user happens to beinterested in minimizing false positives rather than false negatives(incorrect acceptances rather than incorrect rejections), then anadequate solution may lie simply in planning to test fewer variationsabout each of two discrete placements.

In later real-time comparison processing, the invention will searchthrough the downsampled sinusoidal data 14, 14' from the candidate user,to find a closest available match for at least one of the subsets fromthe authorized user. The way in which the subsets are prepared for sucha search, during preprocessing 58, strongly influences both (1) thedata-storage requirements for the system and (2) the time which passeswhile the prospective user is waiting for the invention to make itsdecision.

A tradeoff between these two factors, data storage and real-timeprocessing, leads to two major alternative approaches to managing thesubset preprocessing. At present the limiting consideration is time;however, in the future if much higher processing speeds become availableit may become desirable to instead opt for solutions that reduce storageat the expense of time. Therefore both approaches will be outlined here.

For minimum data storage, it is possible to simply save each selectedsubset in the original form that appears within its respectivesmall-window portion of the template. In this case, the subsets shown asrectangles 31' in FIG. 1 may be identified on a one-to-one basis withthose selected windows, although actually there are likely to be onlythree or four such windows.

This minimum-data-storage case is in fact an extremely important one, sothat actually it is highly desirable to save each subset--and indeed theentire data set for an authorized user--in an abstracted or abbreviatedform rather than in its original form. Accordingly these options areassociated with one major preferred embodiment of the invention.

They are important in particular when a compact, self-contained systemeither must store many templates, for each one of many (e. g., ahundred) authorized users, or must read in a template from a remote databank--or from an identification card (e. g., with magnetic strip or barcode) carried by the user. Either of these cases puts a premium onsmallness of the data file for each user, since full data (and even moreemphatically preprocessed full data) are very costly to store within thesystem for multiple users, or to transmit or store on an ID card. Thisfirst major preferred embodiment is particularly applicable inenvironments where a short additional delay, perhaps a half second to asecond, for calculations is acceptable--automatic tellers, office doors,etc.

In later real-time processing, however, if a subset is presented forcomparison only in its original form, sifting through the candidate data14' for a particular subset is relatively unlikely to succeed. This istrue even if the candidate is in fact the authorized user, since thereis a fairly strong likelihood that the subset of interest has beenrotated or dilated, or both.

Therefore a fair test requires, to begin with, checking each region ofthe candidate data 14' against several rotated forms of the subset undertest--rotated through different angles. In addition to a nonrotatedsubset, the preferred embodiment checks eight nonzero rotations, rangingfrom negative (clockwise) through positive angles.

A fair test also requires checking each such region against severaldilated forms of that same subset--dilated by different factors, rangingfrom values below unity through values above unity. A second majorpreferred embodiment therefore checks, in addition to a nondilatedsubset, six nonunity dilations.

Furthermore each region of the candidate data 14' should be checkedagainst forms of that subset which have been both dilated androtated--covering most or all crosscombinations of those same rotationangles and dilation factors. Taking into account the zero-rotation,unity-dilation cases, the second major preferred embodiment of theinvention preferably uses nine rotations and seven dilations, for atotal of sixty-three cases to be checked.

Each case represents rotation and dilation isomorphically--that is tosay, without change of shape. Each of the sixty-three variants may betermed an "isomorph".

As will be understood, for a representative three subset windows thisworks out to nearly two hundred isomorphs to be checked against eachrecion of the candidate. During real-time processing all these variantforms can be constructed geometrically by the processor, but at thiswriting the additional time occupied in this effort--or the additionalcost of parallel processors to do this work--tends to make this approachprohibitive for high-urgency applications such as weapons or emergencycommunication systems.

Preferably instead, for the present, each of typically three subsets ispreformed (or "premassaged") into each of the sixty-three isomorphs(FIG. 2) described above, and each of the resulting one hundredeighty-nine isomorphs is stored in the apparatus. This represents thetradeoff that yields minimum processing time but maximum storage, and aspointed out just above is associated with a second major preferredembodiment; it is particularly appropriate to single-user environments(e. g., personal weapons) where extremely rapid verifications arerequired with very high certainties.

For a clearer conceptual grasp of the multiple-isomorph preformationtechnique, an original subset 31 (FIG. 2) may be regarded as at thecenter of an array of several rotations (shown in the drawing as arrayedfrom left to right in order of increasing counterclockwise angularvalues) and several dilations (shown as arrayed from bottom to top inorder of increasing dilation). Rotations are emphasized in theillustration by radial tick marks at the four compass directions of theoriginal.

Negative or clockwise rotations thus appear to left of the centrallyplaced original 31, and dilations by factors less than one--or in otherwords contractions--appear below that central original 31. Purerotations are in the same row directly to left and right of the centraloriginal 31, and pure dilations are in the same column above and belowit.

Crosscombinations make up the remainder of the illustration, forinstance an isomorph 31'm of maximum negative rotation combined with atwo-thirds-of-maximum positive dilation being shown near upper left.Whereas an original subset 31' (FIG. 3) is always in the originalrelation to its full template 21, in general it will later be found insome other relation (if at all) in the candidate data 11.

Thus the same above-introduced isomorph 31'm (FIG. 2)--clockwise-rotatedand rather strongly dilated--may appear in a different position in thecandidate data (FIG. 3). The association of such a structure 31'm withboth the template 21 and candidate data 11 thus links the two data setstogether, and reveals how an isomorph 24 of the entire template 21 mustbe selected and disposed for a fair comparison. Just such information 38is what is sought by the global search 32-37.

As will be clear to those skilled in this field, any of a great varietyof compromises may be struck. These may involve--merely by way ofexample--storing all the rotational variants but constructing all thedilational variants on the fly, or vice versa; or storing certain of therotational variants and constructing others as perturbations of thestored ones, etc.

Thus a third major preferred embodiment is associated with a family ofsuch tradeoffs, one tradeoff in particular involving use of sevenrotations and three dilations for a total of twenty-one isomorphs ateach subset 31'. Another tradeoff is performing most of the derivations28, 29, 22', 22", 31 on the fly.

For the above-mentioned second major preferred embodiment illustratedrectangles 31' in FIG. 1 actually represent a considerably larger numberof stored variants of some three subsets or windows selected 31 from thetemplate 21. This preparation pays off handsomely later, in a blindinglyefficient search through the candidate data 14' for all one hundredeighty-nine isomorphs, constant-shape variants.

For maximum search efficiency it is advantageous to store the Fouriertransforms of the subwindows, rather than their direct spatialrepresentations. As will be seen, this preference saves time in thereal-processing stage because the procedure preferably uses thetransforms.

Returning briefly to the first major preferred embodiment mentionedabove: storage of templates in abstracted or abbreviated form (e. g.,level-downsampled to two-bit or binary data) does require care to avoidloss of ultimate performance. I have found that such storage need notimpair accuracy if the data are properly processed after retrieval.

In particular, routine template-data steps of bandpassing, normalizingand smoothing should be performed on the abstracted data to as nearly asfeasible reconstitute the original information set. These steps beatdown the high frequencies introduced by storage in one- or two-bit form.

Another critical time for success of such methods is preparation forstorage. The raw data should be smoothed, downsampled and normalizedbefore storage.

Selection and stepping of the comparison regions in the globalsearch--In real-time processing, the first (most distinctive) of thesubsets or windows 31' is selected for comparison with the filteredcandidate print 13. In FIG. 1 this function is called "subset stepper"32.

More specifically, the stepper 32 selects a first one of the sixty-threeisomorphs of the first window or subset 31'. In simple spatial terms, itis desired to find a portion, a small region, of the candidate print 14'which most closely corresponds to this first subset isomorph 31'.

One straightforward way of finding that most closely correlatedcandidate-print region would be to simply pass the first subset isomorph31' systematically over the whole candidate print. While doing this, itwould be necessary to keep a record of the quality of the match betweenthe isomorph 31' and each portion of the candidate print traversed.

For example, the apparatus might first position or superimpose the firstsubset isomorph or variant 31' in the upper left-hand corner of thecandidate print, and measure the similarity (goodness of correlation)between the first variant 31' and the superposed candidate region. Thenthe apparatus would record that correlation value in association withthe position. Next the first variant 31' might be shifted to the rightby a distance equal to some fraction of the typical ridge spacing, andthe measurement and recording repeated for this new position. When thecomparison process reached the right-hand edge of the candidate, theapparatus would shift the first variant 31' down by, again, a distanceequal to some fraction of the typical ridge spacing, and then again scanacross the candidate print while recording correlation values at eachposition. This entire sequence would be iterated until the comparisonhad been completed for all rows.

From the recorded data the system could then pick the best correlationvalue, and retrieve the position information associated with that value.The result would be a specification of both (1) the best correlationposition for the first subset variant 31' and (2) the quality of thecorrelation there.

The scanning-and-recording procedure described to this point is closelyequivalent to the mathematical procedure of convolving the candidateprint with the first variant sub-window. As can be seen from the abovedescription it entails a very significant amount of processing time,though it only finds the best correlation for just one of the plausiblerotations and/or dilations of the first subset.

With the data expressed in sinusoidal terms as previously mentioned, thesame output information can be found much more efficiently by search forthe correlation in Fourier space, as follows. First the Fouriertransform of the candidate print is multiplied by the Fourier transformof the particular rotated, dilated subwindow of the template.

Then the resulting product is back-transformed, and the resulting realarray holds the quality of correlation for each position of interest--i.e., for each position in the candidate print, just as if found bystepping across and down as described above. In this array, the locationof the maximum correlation value represents position in the candidateprint, and the value itself is the quality of correlation at thatposition.

The output array of the back-transform actually holds data that is theequivalent of spatial stepping at intervals equal to the dataspacings--i. e., in view of the previously mentionedperiodicity-controlled downsampling 13', finer intervals than the ridgespacings. Thus the procedure yields the best-match position of thesubset in the candidate, and the quality of the match.

From a purely mathematical point of view, this two-step process might bedeemed equivalent to convolving the candidate with the subwindow--but,if so, only in the sense that mathematical proofs are available to showthe equality of the output numbers. In practical terms (and patentterms), to the contrary, the Fourier method is not at all equivalent:the process itself is extremely different, and the result includesobtaining the desired information in a far shorter time and with manyfewer computer transactions or steps.

Thus this Fourier process is preferable to direct comparison of thespatial data because it is much more efficient. In preparation for thisprocess, as mentioned earlier, the numerous subwindows of the templateare preferably stored as their Fourier transforms, and the candidateprint too is Fourier transformed--just once, at first entry to thelocationestimating stage 34.

For best results some positions in the candidate print in other words,some values in the array--are excluded from consideration. The apparatusshould not be allowed to select regions that are subject to edgeeffects, in particular, or any other systematic major corruptinginfluence.

The Fourier-transform procedure itself has alternative versions. Inparticular, for greatest efficiency, rather than a two-dimensionalFourier transform the invention can calculate two successive transformsof the so-called "Fast Fourier Transform" (FFT) type, one for each ofthe two dimensions of the candidate print.

The invention as described to this point thus finds the region 38 (FIGS.1 and 3) of the candidate print that most closely matches the firstsubset 31' of the template, taking into account an ample range ofrotations and dilations--i. e., a best-matching isomorph 31'm. In theprocess the invention also finds a measure of the quality 36 of thatclosest match 38.

If that quality is better than a preestablished threshold, the inventionis programmed to conclude that the found position, orientation anddilation are clear and clean enough for use in the following stages ofthe procedure. At this early stage, the displacement, rotation anddilation thus found are assumed to have affected the entire templateequally--i. e., globally.

In other words it is assumed here that the candidate print may haveresulted from only certain kinds of changes in the template: shift,rotation, and overall change of scale isomorphically (change of sizewhile maintaining constant shape). The apparatus then proceeds to usethis information in an isomorphic adjustment 23, which will be discussedshortly (and which will be a prelude to the next major side calculation41-47, 25-26).

If, however, the quality 36 of the closest match 38 is not better thanthe preestablished acceptable quality, then it is reasonable to concludethat either (1) the candidate print was not made by the authorized useror (2) operating conditions led to some disruption of the authorizeduser's print, particularly in the area of the first subset 31'. Thissecond possibility must be carefully accommodated to avoid falsenegatives--i. e., rejection of the authorized user.

The preset threshold of quality used here does not operate arbitrarilyto cut off analysis, as for example in the Driscoll system. Rather, ifthe candidate print fails the established quality criterion here, theonly conclusion made is that perhaps the failure is just a matter ofunusable data arising from local disruption of the authorized user'sprint. In this case the system is programmed to repeat the stepperprocess 32, but using another subset from the original selection 31 ofsubsets or windows 31' in the authorized-user template 21--in effectsimply looking for usable data elsewhere in the candidate data 14'.

(Similarly, the use of preestablished ranges and intervals of rotationand dilation is not arbitrary, but justified both from experimentalmeasurements and on the basis of physical principle. As to principle,the ranges are established as arising from the amount of rotationphysically permitted in placement, and from the amount of dimensionalchange that can be produced in a fingertip by pressure within normallyencountered variations. These considerations should be contrasted withDriscoll's arbitrary use of a least-squares fit for uncontrolled andunjustified departures from an expected rotation pattern.)

When the invention cannot find an adequate matching position in thecandidate data for any of the sixty-three variants of the first window,it resorts to the next most distinctive window or subset 31' previouslyselected. The invention looks for a best correlation position of dilatedand/or rotated forms of that window.

As with the first window, the process checks numerous variants, ineffect stepping across and down the candidate print with not only thesecond subset but also its isomorphs at each of a series of orientationangles crosscombined with a series of possible dilations. Again from themany resulting correlation measures, the best is selected. It identifiesthe candidate region that is a closest match to the second window 31',and at the same establishes a rotation and dilation assumed to haveaffected the entire template.

Again if this second set of data fails the quality threshold, the systemcan resort to a third, and sometimes (rarely) even a fourth. If usabledata are found with any of these, the system proceeds to the previouslymentioned isomorphic adjustment. If not, still other levels of analysismay be used as fallbacks; however, in testing, my invention has beenfound to operate satisfactorily without resort to such fallbacks. Inother words, the invention has been found to successfully find a usablecorrelation between some one of the subsets 31' and any input data 14'that represent a real fingertip pattern.

Although the foregoing paragraphs describe a particularly efficient andadvantageous technique, various strategies may be adopted to find thebest variant of the best window 31', and best matching candidate-printposition. All such strategies, whether using direct spatial stepping orFourier techniques, are within the scope of my invention and so withinthe sweep of certain of the appended claims.

As indicated above, if the best match to the first subset is of marginalor poor quality the selector/stepper 32 will select another subset, andsimilarly may then select still another. This happens most typically ifthe candidate is an impostor. Thus processing delay is least likely tobe extended when the candidate is actually the authorized user--acollateral benefit of the previously mentioned operating assumption thatthe candidate is the authorized user.

It is possible, however, that the first subset cannot be matched to anyregion of the candidate print even though the candidate is authorized.This failure may perhaps be due, for example, to damage, unusuallysevere distortion, abrupt folding (if such folding can occurs orobscuring of the skin--or a piece of dirt or a stain--in that region.

The above-described iteration of the procedure using a seconddistinctive region 31' is intended to deal with this exigency.Preferably the stepper 32 selects the subsets 31' in decreasing order ofdistinctiveness, and typically the second subset is only somewhat lessdistinctive than the first. Therefore only a slight loss of certainty inoverall result 54-57 is suffered by resort to the second subset.

If the candidate is not the authorized user--and only rarelyotherwise--the stepper may proceed to try a third and successive subsets31'. Eventually the best (or most typically for an impostor the leastpoor) of the subset/placement combinations is selected for use, and aswill be understood the subset in this case is--relatively speaking--notvery distinctive.

If, to the contrary, two or more of the subsets 31' yield comparablyacceptable (but both rather poor) isomorphs, my invention could attemptto resolve this ambiguity by repeating the procedure for these twosubsets. For this situation, however, in principle the two subsets orregions may be treated concurrently, as a unit--or, alternatively, eachof the two subsets may be considered separately, but with each subset orregion being enlarged by addition of an immediately adjacent region.

Such operation, though well within the scope of the invention and thesweep of certain of the appended claims), has been found unnecessary.The preferred embodiment accordingly includes no such hybrid-subsetprocedure.

Isolation and use of the best overall match: isomorphicadjustment--Eventually the stepper 32 settles on a subset-and-isomorphcombination 31'm, 38 (i. e., combination of subset with location,orientation and dilation) of a single or enlarged composite region thatyields the best quality-of-match index 36. At this point the focusshifts from selection of the subset-and-isomorph pair to use of theisomorph alone.

Thus the iterative procedure 32-37 produces an output that is theisomorph 38 from the best subset-isomorph combination. Again, thisisomorph 38 represents the shift, angling and expansion of the template21 which make the template best match the candidate 11 in the vicinityof the selected subset of template data.

As will be seen, there is a possibility that it is only in this vicinitythat the template best matches the candidate. In fact, a particularlyadvantageous aspect of the present invention is an ability--as will befully explained below to deal with this possibility. At this stage,however, this best-match information is all that has been assembled.

Therefore this best-estimated position/angle/scale combination 38 isapplied 23 as a correction to the template signal 22--forming anadjusted template 24 (cf. FIGS. 1 and 3) that is more fairly comparablewith the filtered candidate data 13. In short, following the globalsearch 32-38 is an isomorphic adjustment 23.

In the isomorphic adjustment, as the name conveys, no change of shapeoccurs--but the entire template signal 22 (i. e., the templatethroughout all of its regions) is shifted, cocked, and dilated orcontracted, to form an isomorph 24 of the entire template 21, thatmatches as nearly as possible the corresponding features 38 of thecandidate print as found in the selected window 31'. Again, while itmight be supposed that it would be reasonable to adjust or perturb thefiltered candidate data 13, 14, the philosophy of the invention is tomodify 23 the template data 22 preparatory to the comparison.

Reasoning behind this philosophy may now be better appreciated: thetemplate is relatively cleaner and clearer, and these properties arereasonably well retained in its adjusted form 24. Adjustments to thecandidate data 13, 14 would interact with its relative noisiness, andstatistically speaking through second-order effects would disturb thelikelihood of a match.

The total area imaged in the candidate print 11 cannot be closelycontrolled to match the template 21--and the template furthermore isshifted, angled and dilated. Naturally when the two data fields 14, 26are eventually overlaid for comparison some areas of each data fieldwill fall outside the other, and therefore be unusable.

As in all print-analysis systems, comparison will then proceed on thebasis of the remaining areas, those areas which coincide, or in otherwords what may be called the "usable" or "overlapping" data 124 (FIG.3D. In the conceptual illustration, the coarse hatching is only intendedto help identify the overlap region 124, not to suggest fingerprintridges or the like--which of course are much finer. (The exact extent ofthe overlapping data cannot actually be known until both templateadjustments 23, 25 are complete.

In the Driscoll and Denyer patents, very small data excerpts fromtemplate and sample are used in proceeding directly to a final decision.As pointed out earlier, reliability of such hasty conclusions appearsquestionable.

In the present invention, by contrast, similarly small amounts oftemplate data 31' have been used, in the global search and isomorphicadjustment, in a very different way--namely only to obtain anintermediate result. That result is a "once-adjusted" template 24 whichis more fairly comparable with the candidate image data 11-14.

All of the overlapping data in this adjusted template 24, which is tosay essentially all the overlapping data in the original template 21,will eventually be used. Furthermore, all these data will be used incomparison with essentially all of the overlapping data 14 from thecandidate--i. e., excepting only the data points removed 13' asredundant.

Demodulation, gradient search for distortion, and distortion adjustment:purpose--As explained above, the isomorphic correction 23 adjusts theentire template based upon relative placement in just one small region.(Even two "subsets" used together would remain a small fraction of thewhole image.)

Therefore, even if the candidate is in fact the authorized user, therestill exists a crucially important potential for mismatch between theadjusted template 24 and candidate data 14. That potential resides inthe possibility of twisting or other deformation in the candidate print.

In other words, the candidate user's finger may have been applied to thesensor surface in such a way as to distort the overall pattern. Suchdistortion consists of differential offsets, rotations and dilationsinternal to the pattern.

No single isomorphic adjustment can possibly take account of suchinternal differential effects. It is believed that thisinternal-distortion phenomenon may be most to blame for failure toreliably verify presence of an authorized user--false negatives--in eventhe most highly sophisticated of prior-art systems.

Again the Driscoll patent seeks to deal with these phenomena by allowingfor, and searching for, small movements of a secondary and/or tertiarywindow relative to expected position. The system of Driscoll apparentlyis limited to such displacements that can be interpreted as part of anoverall rotation of the print.

Driscoll does use a least-squares fit to find the best position for anoverall-rotated version of his template, to use in comparison. Such afitting technique may perhaps implicitly permit other kinds ofmovements--isomorphic dilation or differential distortions. Aleast-squares fit, however, would be appropriate if departures frompositions corresponding to an isomorphic rotation were merely "random"error in the larger sense of lacking correlations, lacking even softconstraints.

The present invention proceeds on the basis of a much more completestatistical model than Driscoll's methodology implies. The presentinvention automatically applies a kind of relatively low credence, on asliding scale, to information that has a relatively high degree ofinconsistency--but without entirely discarding such information.

Although some uncorrelated measurement error may be present, there is nobasis for assuming that the entire amount of departures from predictedpositions are without mutual correlation. Different portions offingertips are not understood to undergo relative displacements that areuncorrelated.

To the contrary, different portions of fingertips are understood to bephysically interconnected by skin and flesh, interrelated through theirinteractions with skeletal members, and otherwise coordinatedsystematically. Furthermore the use of a least-squares fit, beingdivergent from the reality of skin-pattern internal relationships,cannot provide meaningful guidance for either assessing or limiting thecharacter or magnitude of relative movements other than those foundthrough isomorphic rotation.

The Denyer patent too speaks in very general terms of making allowancefor such movements. It offers little or no guidance as to how suchallowance might be made.

What both these prior systems fail to provide is any systematic basis,certainly any principled theoretical basis, for constraining the amountof "allowance" for these movements that is permitted. This failing iscrucial, for inadequate "allowance" will result in turning away anauthorized user, but given enough unfettered "allowance" almost anyprint will match almost any other.

Of course some experience may be brought to bear in making an educatedguess about amounts of rotation or twisting that seem plausible, andamounts that seem too permissive and thus too likely to grant access toimpostors. The measurement space in which such prior-art guesses must bemade, however, appears very ad hoc or addressed to a particularphysical--immediacy essentially a form of designing at the drill press.

The proper extent of such "allowance" is therefore not readily amenableto quantification or to statistical analysis, and this fundamentallimitation aggravates the previously noted limitation of making finaldecisions based on a small fraction of the available information. Aswill be seen the present invention, by contrast, is able to relate theamount of solidly expected variation--through direct application 18, 18'of the a priori statistics 17--to the measurement preparations 44 andfinal-decision preparations 52.

The assessment and use of this sometimes-so-called "prior portion" 17 ofthe expected signal statistics advantageously tend to favor smoothnessin the distortion field as estimated. The prior statistics rest on animplicit assumption that the distortion field contains some correlationstructure--some physically based interrelationship between what happensin one part of the field and what happens in another.

As noted above, different portions of the skin pattern are, after all,physically interconnected--so that each part pulls on each other part(and that "other part" pulls back). The prior statistics thus quantifythe degree to which individual displacements (which in the aggregateconstitute the distortion field) are correlated with each other.Preferably a Fourier-space model is used for the prior-portionstatistics 17.

With some of the hardest work done in the global search 32-38 andisomorphic adjustment 23, my invention is now able to very efficientlyisolate 42-47 and adjust 25 (cf. FIGS. 1 and 4) the template fordistortion. In a very rough conceptualization, this is accomplished byapplying 25 (FIG. 4) the distortion field 45 to the once-adjustedtemplate 24, to obtain a distortion-corrected template field 26.

The distortion field 45 (FIG. 4) also is roughly conceptualized as afield of displacements 45a, for example moving fixed vertical grid lines45" symbolizing the structure of the frame of reference itself, i. e.the web of the skin as distinguished from its pattern of ridges andtroughs) to left or right so that the grid lines 45" assume new forms45b. Arrowheads 45a representing the individual displacements are inmany portions of the drawing very short, and so can be seen as only verysmall arrowhead tips.

The distortion field 45, 45a has been drawn very simplified, so thatthere are no displacements of the horizontal grid lines 45'. The drawingdoes show, however, that on balance the overall amount of leftward andrightward shifting is about equal--as it should be, since any isomorphicdilation or contraction should have already been incorporated into theisomorphic adjustment 23 which formed the first-adjusted template 24.

The symbol"x" in FIG. 4 is not to be misinterpreted literally as anactual multiplication: though some complex multiplication is involved,that would be an oversimplification; rather the symbolism ofmultiplication is only intended at a rough conceptual-analogue level torepresent application of a distortion field 45. The distortion-correctedfield 26 will later be used as a matched filter in the final comparison51.

To extract 42-44 the distortion 45 and so prepare the data for thisnonisomorphic adjustment 25, I first treat the distortion 45 as if itwere a data signal impressed upon a carrier wave--in other words, as ifthe distortion were a relatively slowly-varying information signalmodulating a carrier.

The carrier in this situation is the relatively higher-spatial-frequencyridge/groove pattern of the natural fingerprint, with the finger at restor undisturbed by differential stresses. Two clarifications are needed:

First, it must be recognized that in the final analysis, literally thefinal analysis 51-56, what is of interest is the ridge/groove patternrather than the distortion. The focus upon the distortion at this pointis only temporary and only for purposes of isolating and then cancelingit--just as the global search isolated placement/dilation so that itcould be globally abut isomorphically) canceled.

Second, not only the distortion but also the "instantaneous carrier"(local harmonic content of the ridge/groove pattern) varies stronglyfrom place to place within the candidate image 13. Hence it must beunderstood that distortion will necessarily be extracted as a vectorfield, varying over the image area, not a single global parameter andnot even a scalar field--and the "carrier" too must be treated as afield with many strong local variations.

Obtaining a "carrier" for use in demodulation--Fortunately it is notnecessary to determine what this varying carrier field is, in thecandidate image 13. Instead the authorized-user template 21 is taken tobe the carrier for the candidate data.

Properties or characteristics of the template 21 needed to implementthis approach can be found in advance, during preprocessing 58. Part ofthis is done by in effect mapping 28 the local ridge spacings andorientations, and saving the resulting magnitudes and directions asvector wavenumber fields 29.

Here too the assumption that the candidate is the authorized user is putto major advantage: the template 21 is assumed to be the carrier of adistortion field, a vector field, in the candidate 11, 13. The vectorwavenumber fields 29 of the template represent the spatial frequenciesof that carrier.

Once again, if the candidate is not the authorized user, these latterassumptions fundamentally become gibberish and the ensuing correlationmost commonly fails dramatically.

Demodulation of the distortion field--My invention next proceeds toactually estimate directly, in three steps 42-44, the entire distortionfield 45. The first step 42 is demodulation to obtain an intermediateresult, namely a complex field whose phase is sensitive to the assumedvector distortion field.

For this purpose, forms 41, 41' of the template 21 are needed thatcontain information about both the ridge locations (with their spacings)and their orientations. Stated first very simply, multiplying thetemplate form(s) 41, 41' and the candidate data 14" together yields thedesired intermediate field 45.

The original template 21 (as well as the once-adjusted template 24)taken by itself is passed 41 to the demodulation process 42, but lacksphase information that is needed for such a procedure. For this reason Ibegin by constructing somewhat synthetic or artificial forms 41" of thetemplate that include such phase information.

More specifically, the template 21 (the carriers is first expressed in amodified form, which is obtained through multiplication of its spatialgradient field 22' by its own vector wavenumber field 29: ##EQU1## Thispreliminary product represents a scalar 22" that is in quadrature withthe template.

By the phrase "in quadrature" I mean 90° out of phase, or using radianangular measure ρ/2 out of phase. In other words the scalar 22" found bythis multiplication process is everywhere in the pattern inherently onequarter of a spatial wavelength offset from the basic template. Thedenominator normalizes the expression; thus the quadrature form differsonly as to phase, not as to amplitude.

It is known that a quadrature form of a periodic positional signal, usedin conjunction with the basic positional signal itself, can yielddirectional or phase information for use by automatic apparatus indetermining, for example, a direction of motion. In my invention a likeunderlying principle is used, albeit in a conceptually very remotecontext, to enable the algorithm to keep track of the direction in whichfeatures of the candidate print are offset from features of thetemplate.

If not for the reentrant character of most skin patterns of interest, itwould be sufficient to use a quadrature form 22" of the template in justone single version. The typical closed patterns 62 (FIG. 2) and whorlsfamiliar in fingerprints, however, render such a simple representationinadequate for the following reasons.

In a generally linear region 61 of a print, of course if one couldmonitor, along a path very generally from ridge 75 to ridge 75', itwould be natural to expect continuity of phase-gradient direction 65,65'--i. e., the direction locally perpendicular to each ridgeline, inwhich phase increases. By the phrase "continuity of phase-gradientdirection" here is meant the property of the direction being consistent,or in other words not reversing except perhaps where it is near zero).

Such continuity as illustrated by phase-direction arrows 65, 65' nearthe left end of the drawing, is expected irrespective of the fact thattwo adjacent, parallel ridges 75, 75' happen to open up into a whorl 62,and as shown even a whorl which includes distinctly closed loops.

The phase-gradient directions 65, 65' for both such adjacent parallelridges 75, 75'--which happen to span such an enlargement 66--can betraced toward the right along the respective ridges 75, 75'. Eventuallya point 72 is reached at which the "two" ridges 75, 75' are found tohave been actually different tails of just one common ridge 75-75'. Atsome such place along the way, therefore, the initially commonphase-gradient directions 65, 65' are found to be directed oppositely68, 68'. If this phenomenon is not somehow controlled, the entire phasefield becomes unmanageably ambiguous as can be seen by tracing theupward-pointing phase arrows 65 around the loop.

Such tracing finds likewise upward-pointing arrows 67 across the top ofthe whorl 62, rightward pointing arrows 68 along the right end 64 of thepattern, and downward-pointing arrows 69 back across the bottom to theleft end 61. Even in this latter region 61 of generally parallel andrectilinear ridges 75, 75' the downward arrows 69 are oppositelydirected from not only the upper set of phase arrows 65 above thedivision line 66 but also the lower set 65'. That lower set, as will berecalled, is associated with the identical ridge line 75' below thedivision line.

To deal with such potentially troublesome discontinuities, my inventionforms not just one but at least two quadrature forms 22" of thepreviously discussed gradient-times-wavenumber product--which is ascalar. Furthermore in operation the algorithm of my invention mustautomatically select a particular one of the plural cuadrature forms foruse.

Preferred embodiments of my invention make this selection based uponmonitoring for phase discontinuities of the sort illustrated. Themonitoring is preferably carried out by detection of sudden reversals inthe sign of the wavenumber field 29.

These sign reversals can be found during preprocessing 58, and theirlocations marked by warning flags 73, 74 a specified distance from eachdiscontinuity 72--in each direction along an axis transverse to thediscontinuity. Preferably this work is done during preprocessing, information of the template, moving one step at a time in either the x ory direction, in real space--while requiring neighboring values to besubstantially continuous, and setting up the flagging in an associatedwavenumber field 29.

In terms of the FIG. 2 example, continuous processing along a vertical(v) direction locates the discontinuity 71 at a height 72 in thepattern.

Later in actual candidate processing, with the wavenumber fielddownsampled 43 onto the coarsest grid, the system watches for the flags73, 74 only at right angles to the direction v selected previously forimposition of continuity. This strategy enables the processing to staysome distance away from a discontinuity.

For computational (and tutorial) convenience I express the template 21as a complex number. I set the real part of this number equal to thedirect spatial form of the template 21, 22, and the imaginary part equalto the selected one of the preliminary products, the in-quadraturescalars 22", just described, i. e.:

    template'=template+i.(quadrature form of template),

where i is the base of imaginary numbers, the square root of negativeone.

Both the real 22 and imaginary 22" parts of this variable are thensubjected in real processing time to the isomorphic adjustment 23. Theadjusted results 24, 24' are passed 41, 41', as already suggested, tothe demodulation process 42.

Here the complex variable template' as mentioned above is multiplied bythe candidate data 14", yielding a new complex variable in which isembedded phase information related to the distortion field that is beingsought. The distortion field in fact is fundamentally aphase-displacement field, though in some minority of cases the phaseshifts due to distortion exceed a half-wave (180°, or π radians) andeven a whole wave (360°, or 2π radians).

The cases in which maximum distortion thus exceeds half of a ridgespacing, although ordinarily in the distinct minority, are by no meansnegligible. To the contrary they are extremely important in successfulpractice of my invention I have found experimentally that if such casesare neglected the resulting ambiguity of displacement direction--andgross errors in implied character of the candidate print--are oftencatastrophic to recognition of the authorized user.

The new complex variable resulting from this demodulation(multiplication) step may be represented so:

    exp {i.(distortion field).(wavenumber field)}+noise,

in which "exp" means the exponential function, and "distortion field" isthe unknown random field 45 quantified statistically by the a prioridata 17.

The factor "wavenumber field" represents the same known vectorwavenumber field 29' used earlier in constructing the quadrature form ofthe template. The additive term designated "noise" corresponds to theresidual effects of all features of the candidate data that do notrepresent the local sinusoid associated with the ridges and troughs ofthe candidate user's skin pattern.

The immediate object of the inquiry is to determine the distortionfield. As can be seen, the "noise" term obscures the desired answer.

If one wishes to find the true answer it is very desirable to at leastmake some allowance for the full expression, including the "noise" term,presented just previously--since that full expression is the quantitywhich has been found through the demodulation process. The preferredembodiment does makes allowance for the measurement noise bydownweighting the demodulation locally, in general proportion to localnoisiness in the data--or, in other words, by discounting informationfrom regions known to be noisy.

Of course it would be a great deal easier, in a manner of speaking, tosimply use a "fitted" phase without regard to any distortion field orwavenumber field--that is to say, a phase which appears to account forobserved mismatches between template and candidate, but is not toolarge. Doing so, however, would be in a sense somewhat analogous to the"allowing" of some plausible amount of translational wandering orrotation in the method of Driscoll, discussed earlier.

It would be very hard to say, based upon any reasoning from firstprinciples, how to constrain such a fitting, or in other words just what"not too large" means. This is analogous to the problem noted earlier,relative to the Driscoll system, of establishing how much translation orrotation is plausible and how much is simply letting in more candidateusers.

One of the particular benefits of the present invention is that itenables estimation of an actual distortion field that is consistent with(1) the assumption that the candidate user is the authorized user, and(2) a term "noise" that corresponds to measurement noise in thecandidate data, and (3) an additional noise term representing amagnitude and degree of smoothness, in the distortion, which is not onlyplausible and not only "not too large" but actually statistically likelyas quantified in relation to the a priori statistics.

Thus by approaching the phase-field or distortion-field determinationfrom this seemingly roundabout direction the present invention placesthe relevant relationships in a form that is amenable to direct use ofknown variabilities in fingerprint placement. The entire verificationprocess is thereby placed on a footing which is far more solid andphysically meaningful than ever possible heretofore.

It remains, however, to say how the distribution field can be extractedfrom the expression presented above. This is by no means a trivialexercise, as it calls for, in effect, inverting a matrix which ismultidimensional--more specifically, having as many dimensions as thereare downsampled 43 data points to be used.

Downsampling for tractable processing--Thus extraction of the distortionfield involves extremely intensive processing. If it were necessary toperform such procedures at full resolution, which is to say on theentire received data set 14" after the first downsampling 13', therequired processing time would be prohibitive in most routine uses. Withpresentday limitations of processing speed it can only be renderedfeasible through a two-part "smoothing and second downsampling" stage43.

Of the two parts of this stage 43, the one that may be regarded as themore fundamental is the second downsampling, to reduce by an additionallarge factor the amount of data to be thus intensively processed.

The earlier downsampling 13' was justified on the basis that the datawas represented in periodic terms, and that use of sampling intervalsmuch smaller than the smallest period represented in the template couldonly produce redundant data. Like reasoning applies to the distortionfield, but the latter is assumed to change far more slowly--an order ofmagnitude more slowly--than the elevation changes corresponding to thebasic ridge-and-groove pattern.

Fortunately the desired distortion field as a practical matter is almostalways a relatively smooth pattern. It is most typically a differentialdilation--such as may be expected from pressing some parts of afingertip more forcefully than others.

In some cases it may also, or instead, partake of a relatively gentletwisting, such as a "C" or sometimes "S" curve--and much more rarelywith an abrupt near-discontinuity, such as mentioned above in connectionwith the need to resort to second or third local subsets 31' in theglobal search.

Consequently a much smaller amount of candidate data, sampledsystematically from the filtered candidate data 14, 14" afterdemodulation 42 suffices to define the distortion field. Thus it isagain reasonable to eliminate merely redundant data by downsampling 43to a much longer sampling interval than used in the first downsampling13'.

In the very occasional case of a considerably more abrupt form ofdistortion, just mentioned, the distortion is so abrupt that it can betreated as an entirely different case--a near-discontinuity, e. g. avery severe local distortion of the skin in a particular region.

As indicated previously, however, my invention is able to dealsuccessfully with such cases. It first avoids them in selection oftemplate subsets 31' for the global search; and it later successfullymatches other very large areas of the print, in the final comparison 51.

This is a major advantage of the use of essentially all available data,data drawn from an entire print--as mentioned earlier--rather than onlyisolated regions. Earlier systems, even relatively sophisticated onessuch as Driscoll's and Denyer's, typically are quite unable to verify anauthorized user when one or more of the most distinctive regions happento be disturbed in this way.

It is believed in some quarters that an actual folding of the skin canoccur, giving rise to an actual discontinuity in the ridge pattern in aparticular region. No amount of continuous distortion can be used toapproximate closely such a violent event, if indeed such events occur,in which some portions of the skin pattern typically are actuallyremoved completely from visibility. It is contemplated, however, thatthe procedure of the present invention is reasonably robust and so candeal with even such extreme cases.

In this second downsampling it is permissible either to downsample fromthe first downsampled data 14 as illustrated, or to downsample from thefuller data set 13. The former, however, will be much faster.

In choosing the second downsampling interval, care should be taken toavoid inadvertently, implicitly limiting the degree and character--e.g., abruptness--of distortion taken to be present. As suggested above,such arbitrary limitation without physical basis can skew the results.

Limits on distortion should arise from the model in use--specifically,by downsampling at sampling intervals which are related to a measure ofthe local rate of relative change of phase in the data. This measureconveniently should correspond to the highest significant spatialfrequencies in typical or representative distortion fields for realcases.

Such information is contained in the statistical a priori data 17.Therefore, to obtain such a measure, the preferred embodiment firstextracts from the a priori statistics 17 an estimate 18" of the powerspectral density for distortion fields generally (in other words, notfrom the candidate data 11 or template 21). It then sets the samplingintervals, as a function of position, in accordance with that estimate18" of power spectral density.

Bandpassing was used in preparation for the first downsampling 13'--notonly for control of noise as such but also specifically to avoiddownsampling to nonrepresentative data points. Similarly it is desirableto smooth the data before the downsampling procedure.

This smoothing is the other, and perhaps the less fundamental, of thetwo parts of the "smoothing and downsampling" stage 43 mentioned above.In the preferred embodiment it is implemented as a low-pass (Fourier)filter--realized with Fast Fourier Transforms. Preferably the smoothingis done as a convolution--with a fixed window in Fourier space--in closeconjunction with the second downsampling.

Estimation of the distortion field: gradient search--My invention hereuses once again an approach that depends upon manipulation of theoverall pattern. Here the pattern is considered as a matrix, and thebest-fit distortion field is sought by an iterative approach.

This approach in effect tests the improvement in fit found by initiallyassuming a distortion field, sequentially making many small changes inthat field--at each point assessing the results in terms of quality offit--and then redirecting subsequent changes accordingly. At each pointthe assumed field is modified in a direction which the processingresults up to that point suggest will further improve the fit.

This iterative approach is somewhat akin to finding the summit of a hillby probing at each point for an uphill slope, and then following thatuphill slope a short distance to the next test point. In fact thegradient of a quality-of-fit function is used in this process.

The "gradient search" 44 used in my invention, however, ismultidimensional. In other words the "hill" is assumed to be a peak inquality-of-fit space, and this space has a number of "dimensions" equalto the number of data points in use--in other words, even after thedownsampling described above, typically some thousands of dimensions.

In the progressive approach to finding the best fit, it is particularlycrucial to avoid taking individual steps that are too large. Apart fromthe relatively straightforward hazard of overshooting the peak (whichcan be correctable in later steps if they are not too large), a muchmore insidious kind of error arises from excessively long steps.

As mentioned earlier, many realizations of skin patterns are subject todistortions which amount, locally, to more than a half wavelength oreven one or more full wavelengths in the pattern. If such a distortionis allowed to develop too rapidly, the only portion of it which is ineffect "visible" is the fractional part remaining after deduction of anintegral number of wavelengths.

It is essential to realize that correlation goes to zero in any regionof the template that is misaligned by only a quarter of a wavelength.Hence, avoiding errors of a half wavelength, or of course anythinglarger than that, is of extremely great importance to successfulpractice of my invention--at least in those cases where sizabledistortions are in fact present.

(Dealing with experimental subjects who may develop helpful habits, forexample gentleness in applying fingertips to sensors, can actuallyseduce an algorithm designer into a trap of complacency with respect tothese larger distortions. In uncontrolled use of the invention of courseno such delicate behavior can be assumed.)

Scaling of the steps to avoid falling into such ambiguities ispreferably achieved by limiting the algorithm's rate of propagation--inthe spatial or frequency domain, or preferably both--outward from theinitially small region of close match ensured by the global search32-37. Thus the search 44 for an estimation of the distortion fieldbegins in a tightly defined region about a distinctive point in thetemplate, and it is allowed to expand slowly stepwise.

The permissible expansion rate depends on ability to extrapolatejudiciously from previous distortions. In the preferred embodiment theexpansion or extrapolation steps are related to the intervals previouslyestablished for use in the second downsampling 43.

Computational burdens in the gradient search are borne by Fast FourierTransforms, which are very efficient. The procedure continues until thewindow has expanded to the whole field.

Isolation and use of the distortion field--The iterations of thegradient search 44 lead to definition of an estimated distortion field45. This field 45 next is subjected to an intermediate upsampling step46, through interpolation--preparatory to use in the distortional ornonisomorphic adjustment 25. This distortional adjustment 25 will form atwice-adjusted template 26, which should provide the fairest possiblefinal comparison 51 with the candidate data 14.

The intermediate upsampling step 46 is necessary because the distortionfield 45 was developed on a very coarse grid due to the seconddownsampling 43, but the twice-adjusted template 26 must be madeavailable at full resolution. More specifically, it is needed atgenerally the same sampling as established on the candidate-data side inthe first downsampling 13'.

Accordingly, what is read out to the distortion-adjustment step 25 is anupsampled version 47 of the field 45; it is this upsampled version 47which is applied 25 to the once-adjusted template 24. The application 25step is done by multiplying together the two complex-valued fieldstemplate' 24 and exp {i distortion field).(wavenumber field)}, andretaining only the real part of the result.

The resulting twice-adjusted template 26 should provide the bestpossible likelihood of a match with the candidate data 14--if thecandidate is in fact the authorized user. If not, then as suggestedearlier the greatest likelihood is that the twice-adjusted template 26will bear little relation to the candidate data 14.

Final comparison, thresholdina and decision--The twice-adjusted template26 and the once-downsampled candidate data 14 are then compared 51. Thisis done by multiplying them together and summing over the image, subjectto inverse weighting 16 based on the candidate-image noise varianceestimates 15. In this process the twice-adjusted template 26, with theassociated twice-adjusted quadrature forms 26' and twice-adjustedwavenumber field 29", constitute and are used as a matched filter. Theresult of the filter process 51 is used to form a major part of the teststatistic 52.

The latter is preferably formed according to the Neyman-Pierson analysisas a ratio of the likelihoods of occurrence of the processed candidateprint data according to two contrary hypotheses--namely, that theauthorized user (1) was and (2) was not the maker of the candidateprint. Based on this "likelihood-ratio" procedure, the above-mentionedtest statistic 52 also incorporates noise statistics 18, once againproviding an opportunity to ground the results in solid reality byapplying the a priori statistics 17 for the distortion field.

(As a practical matter, for easier management of ratios spanning a verylarge range of values I prefer to employ the logarithm of the ratio.This variant is sometimes called a "log-likelihood-ratio" method, whichis in turn familiarly abbreviated to "log-likelihood" method.)

As explained earlier, these data are "a priori" in the sense of notbeing derived from either the candidate print or the authorized-usertemplate. They are not, however, "a priori" in the sense of beingderived from first principles; rather, these data are collectedempirically. (In particular there appears no indication that Driscolltakes into account any such considerations as the a priori term.)

One particularly beneficial property of the Neyman-Pierson approach isthat assessment of the two above-mentioned contrary likelihoods isstraightforward. These correspond rather directly to the probabilitiesof false negatives and false positives, respectively.

In a representative Neyman-Pierson diagram, not particularly associatedwith the present invention, a composite test statistic T (FIG. 6)represents a log-likelihood parameter such as mentioned above. The twogenerally bell-shaped curves 81, 82 at left and right represent theprobabilities of two mutually inconsistent hypotheses.

To relate this graph to the general field of fingerprint verification,for example, the curves 81, 82 might represent the probabilities that aparticular print was formed by, respectively, an impostor and theauthorized user. A diagram of this sort depends strongly on manydifferent experimental facts, particularly including the amount of noiseor experimental error in the system.

The vertical line near the intersection of the two curves representsselection of a particular threshold value T_(T) of the test statistic T.The shaded area 83 extending leftward from that line, under the left endor tail of the right-hand curve 82, represents the probability of afalse rejection of the authorized user--or in other words, as it issometimes called, a "type 1" error.

The shaded area 84 extending rightward from that same vertical lineT_(T), under the right end or tail of the left-hand curve 81, representsthe accumulated probability of an erroneous acceptance of an impostor--afalse acceptance, or a "type 2" error. As will be apparent, the relativesizes of these two types of errors can be adjusted by sliding thethreshold or discriminator T_(T) to left or right.

This very general diagram is characteristic of a great many kinds ofprocesses, and as can be seen the two areas 83, 84 representingerroneous decisions each are here arbitrarily drawn as amounting to afew percent, perhaps as many as eight or ten percent, of the respectiveoverall areas 85, 86 under the two curves 81, 82. That general range ofnumbers appears to be representative of, or perhaps better than, thestate of the art in automatic fingerprint verification apparatus andmethods heretofore.

My invention enables both evaluation and quantitative control of thesetwo kinds of undesirable result 83, 84 quite readily. As a result ofpreliminary work--with expectably some further improvement yet to bemade--the overlap region 83'+84' (FIG. 7) between the two probabilitydistributions 81', 82' is reduced to a small fraction of one percent.

In relation to the present invention, the test statistic T can now beidentified with the like-entitled block 52 in FIG. 1 (see at right inFIG. 7), and the selected threshold T_(T) similarly identified with thethreshold 53 of FIG. 1 gsee at center in FIG. 7). As will be recalled,the desired-certainty threshold 27 is set during preprocessing 58 toaccord with not only the authorized user's preferences as to type oferror least acceptable, but more quantitatively that user's preferredrelative balance or tradeoff between the magnitudes of the two types oferrors.

The improvement provided by my invention is so great that it would bedifficult to draw the two entire curves 81', 82' at such a scale thatthe overlap regions 83', 84' could be clearly seen in the same view (asthe corresponding much larger regions 83, 84 are seen in FIG. 6).Characteristic error probabilities 83', 84' with my invention asdeveloped at this writing are in the neighborhood of 0.001, or one-tenthpercent.

This means that at worst, with the test statistic threshold T_(T) set atan optimum point within the overlap region either the false-negative orfalse-positive rate may be a maximum of that same fraction of onepercent. If the test statistic T_(T) is offset from that optimum point,however, then the particular kind of error of greatest concern to theauthorized user can be made much smaller than that fraction of apercent.

For instance, the threshold T_(T) can be set well above the absoluteoptimum point, in response to a decision by the authorized user to favorfalse negatives 83' (as for example to give particularly high protectionagainst improper use by family members). The probability of a falsepositive 84' is thereby easily made a much smaller fraction of onepercent, for example 0.01 percent, at the cost of, say, a one-percentincidence of false negatives 83'.

Almost as important as the low value of the false-negative andfalse-positive probabilities at their crossover point is the fact thatthis crossover probability can be specified. In fact the probability ofa false positive for any particular setting of the threshold 53 can bequantitatively specified, as can the associated probability of a falsenegative.

Given such information, correlated with the range of settings of thethreshold 53, the authorized user is for the first time able to make afully informed and therefore at least potentially intelligent choice ofthe desired threshold 27. As mentioned previously, the relationshipbetween selected threshold 27 and actual probabilities, or actual levelof desired certainty, is not direct in the sense of a linear or simplemathematical function. The relationship is, however, both monotonic andreadily stated in terms of a calibration scale or a tabulation.

Utilization--In operation a candidate user's finger or toe 90--or palm,or any other surface having a comparable skin pattern--is applied to thesensitive surface 91 of a sensor module 92 (FIG. 8D. The system may beprogrammed to start when a skin pattern is thus applied 57 (see FIG. 1,bottom left) to the sensitive surface, or if desired may be providedwith a separate start-up switch (not shown).

The sensor module 92 develops an electronic image 11 (see also FIG. 1).The sensor unit 92 advantageously may be an optical detector array--e.., one of the types described in the Bowker and Lubard patent documentmentioned earlier--or may be any other type that yields a suitablecandidate-user image data set 11, for instance a capacitive,variable-resistance, or ultrasonic detector.

I prefer to use an optical-fiber prism as described by Bowker andLubard. In view of the current economics of large sensors andoptical-fiber tapers, however, I currently prefer to use a relay lens(rather than such a taper) to focus the image from the output end ofthat prism onto a small sensor.

Associated with the sensor module is a read-only memory or ROM (or aprogrammable ROM, EPROM) 93, which holds the authorized user's template21, 22 (FIG. 1) and associated data 22", 29--as well as thedesired-certainty threshold 27 and the a priori statistics 17. (In FIG.8 these several callouts are abbreviated "21 &c.") The candidate data11, template data 21, and related data sets all flow to a programmed orprogrammable microprocessor or "central processing unit" (CPU) 94.Stored in the ROM 93 or in the CPU 94, or partly in each, is the programdescribed in this patent document.

The portions 91-94 of the apparatus discussed so far--and certain otherportions if desired--are advantageously made self-contained and forcertain applications also made portable. Accordingly a battery or otherportable power supply 95 may be included with the sensor module 92, ROM93 and CPU 94, and interconnections incorporated, all within a housing96.

In such a case the output enablement signal 55e (also see FIG. 1) mightbe the only output from the apparatus. That output passes toaccess-control module 97, which may include a suitable local or remoteswitching device for passing an actuation signal 98 to utilization means99.

The utilization means 99 represent a facility, apparatus, means forproviding a financial service, and/or means for providing or receivinginformation.

Merely by way of example, and without any intent to limit the types ofthese devices which can be controlled in this way, the utilization meansmay be and/or may include a cabinet, home, office, military or othergovernmental installation, educational institution, weapon, computer,vehicle ignition and/or entry, automatic teller machine, credit system,time-and-attendance system, or database information service.

As shown the self-contained unit 96 may provide an enablement ordecisional signal 55e to a discrete access-control unit 97. In manysystems, however, the access-control module 97 is preferably integratedinto the self-contained unit 96--in accordance with security-enhancingintegration principles described in the aforementioned document ofBowker and Lubard. Similarly the whole of the print-verifying andaccess-control devices 96, 97 is advantageously integrated into theutilization means 99.

In both cases the general idea of such integration is to make thesecurity aspects of print-verifying control relatively invulnerable tobypassing. That is to say, integration of the whole system can provideresistance to insertion of a jumper, short, or other form of injectedsimulated access-control signal 98 at the utilization-means 99 input.

Thus for instance in a weapon, bidirectional information flow betweenthe CPU 94 and a detonator 99 within each projectile (bullet etc.) canprevent tampering with the intermediate firing mechanism. In a vehiclethat has a distributor or other ignition module 94 directly associatedwith the combustion system, automatic exchange of information betweenthe CPU 94 and that ignition module can deter bypassing of the securitysystem.

In a credit, time-and-attendance, or information-dispensingdatabase-access system, similarly, the CPU 94 should be programmed toparticipate in a dialog with the central computer 94 of the credit etc.system. Such a dialog ideally is conditioned to verify not only theidentity of the user but also the integrity of the connection betweenthe CPU 94 and the central system.

In view of the foregoing, further examples will now occur to thoseskilled in the art.

In the course of experimentation it has been found helpful to exploitsome curious phenomena relating to fingertips of some subjects. First,it has been noted that in some people a particular fingertip--includingin one case the index finger--cannot yield a usable template.

This appears to be due to diverse causes such as, at one extreme,extraordinarily dry flaky skin, and at the other extreme heavy sweating.Somewhat surprisingly such effects are sometimes localized in just onefinger i. e., they involve differential sweating as between differentfingers--and so are readily overcome by using a different finger of thesame subject.

Although I have observed very little correlation between fingerprints ofidentical twins, a significant partial correlation appears betweendifferent fingers of a single subject. Much lower false-acceptance ratesoccur if an individual can pass the verification procedures with both oftwo different fingers; this offers a methodology for reducing type 1errors, which is intriguing in that it may not adversely affect type 2errors in like proportion.

The methodology essentially makes use of multiplicative statistics. Arelated application may reside in the fact that much lower falserejection rates can be achieved where the system is set up for use byeither of two fingers.

It will be understood that the foregoing disclosure is intended to bemerely exemplary, and not to limit the scope of the invention--which isto be determined by reference to the appended claims.

What is claimed is:
 1. Apparatus for verifying the identity of a personby comparing test data representing a two-dimensional test image of thatperson's skin-pattern print with reference data derived from atwo-dimensional reference skin-pattern print image obtained during aprior enrollment procedure; said apparatus being for use in the presenceof an assumed distortion of the test image relative to the referenceimage; and said apparatus comprising:means for deriving from the testdata corresponding multilevel test data that are bandpassed andnormalized; means for estimating the assumed distortion of the testimage relative to a reference image; means for comparing portions of thebandpassed and normalized multilevel test data with the reference data,taking into account the estimated distortion; means responsive to thecomparing means for making an identity-verification decision; andnonvolatile memory means for holding instructions for automaticoperation of the foregoing means.
 2. The apparatus of claim 1:furthercomprising means for extracting from the test data an estimate of noisevariance in the test data as a function of position in the test image;and wherein the estimating means and the comparing means perform saidestimating and said comparing, respectively, as a function of position;wherein the estimating means or the comparing means, or both, comprisemeans for taking into account the estimated noise variance.
 3. Theapparatus of claim 1, wherein:the estimating means comprise means forusing a maximum-likelihood method to estimate the distortion field. 4.The apparatus of claim 1, wherein:the estimating means comprise meansfor demodulating the test data preliminary to extracting a distortionfield therefrom.
 5. The apparatus of claim 1, wherein the estimatingmeans comprise:the estimating means comprise means for avoiding errorsdue to phase shifts greater than half the local periodicity of theassumed carrier field.
 6. The apparatus of claim 1, wherein theestimating means comprise:means for providing an assumed carrier fieldfor use in demodulating the test data; means for analyzing thedemodulated test data to approximately ascertain distortion associatedwith the demodulated test data.
 7. The apparatus of claim 1, wherein:theestimating means comprise means for downsampling the test data accordingto anticipated degree of abruptness of at least one type of distortion,in preparation for estimating the distortion.
 8. The apparatus of claim7:wherein the estimating means comprise means for downsampling the testdata before estimating the distortion; further comprising means forapplying the estimated distortion to approximately equalize the test andreference data with respect to the assumed distortion; furthercomprising means for interpolating the estimated distortion, to upsamplethe estimated distortion for use in the applying means; and wherein thecomparing means compare the thus-approximately-equalized test andreference data.
 9. The apparatus of claim 1, wherein:the estimatingmeans comprise means for using a gradient search to estimate thedistortion.
 10. Apparatus for verifying the identity of a person byliterally and directly comparing a test data set representing atwo-dimensional test image of that person's skin-pattern print with areference data set derived from a two-dimensional reference skin-patternprint image obtained during a prior enrollment procedure; said apparatusbeing for use in the presence of an assumed geometrical distortion ofthe test image relative to the reference image; and said apparatuscomprising:means for estimating the assumed geometrical distortion ofthe test image relative to a reference image; means for literally anddirectly applying the estimated distortion to approximately equalize thetest and reference data sets with respect to the assumed geometricaldistortion; means for literally and directly comparing the test data setwith the reference data set, taking into account the estimatedgeometrical distortion; wherein the comparing means literally anddirectly compare at least major fractions of thethus-approximately-equalized test and reference data sets themselves, asdistinguished from individual very small subarravs thereof, and also asdistinguished from mere measures of correlation between the sets, andalso as distinguished from mere measures of distortion of one or bothsets; means responsive to the comparing means for making anidentity-verification decision; and nonvolatile memory means for holdinginstructions for automatic operation of the foregoing means. 11.Apparatus for verifying the identity of a person by comparing test datarepresenting a two-dimensional test image of that person's skin-patternprint with reference data derived from a two-dimensional referenceskin-pattern print image obtained during a prior enrollment procedure;said apparatus being for use in the presence of an assumed distortion ofthe test image relative to the reference image; and said apparatuscomprising:means for estimating the assumed distortion of the test imagerelative to a reference image; means for comparing the test data withthe reference data, taking into account the estimated distortion; meansresponsive to the comparing means for making an identity-verificationdecision; means for applying the estimated distortion to approximatelyequalize the test and reference data with respect to the assumeddistortion; and wherein: the comparing means compare thethus-approximately-equalized test and reference data; and the applyingand comparing means comprise means for using the estimated distortion togenerate a matched filter for use in forming a test statistic; andfurther comprising nonvolatile memory means for holding instructions forautomatic operation of the foregoing means.
 12. Apparatus for verifyingthe identity of a person by comparing test data representing atwo-dimensional test image of that person's skin-pattern print withreference data derived from a two-dimensional reference skin-patternprint image obtained during a prior enrollment procedure; said apparatusbeing for use in the presence of an assumed distortion of the test imagerelative to the reference image; and said apparatus comprising:means forestimating the assumed distortion of the test image relative to areference image; means for comparing the test data with the referencedata, taking into consideration the estimated distortion; meansresponsive to the comparing means for making an identity-verificationdecision; and means for extracting from the test data an estimate ofnoise variance in the test data as a function of position in the testimage; and wherein: the estimating means and the comparing means performsaid estimating and said comparing, respectively, as a function ofposition; the estimating means or the comparing means, or both, comprisemeans for taking into account the estimated noise variance; and thetaking-into-account means comprise means for weighting the importance ofthe estimating or comparing, or both, as a function of position inaccordance with the noise variance estimate for the correspondingposition; and further comprising nonvolatile memory means for holdinginstructions for automatic operation of the foregoing means. 13.Apparatus for verifying the identity of a person by comparing test datarepresenting a two-dimensional test image of that person's skin-patternprint with reference data derived from a two-dimensional referenceskin-pattern print image obtained during a prior enrollment procedure;said apparatus being for use in the presence of an assumed distortion ofthe test image relative to the reference image; and said apparatuscomprising:means for estimating the assumed distortion of the test imagerelative to a reference image; wherein said estimating meanscomprise:means for using a maximum-likelihood method to estimate thedistortion field, and means for using the maximum-likelihood-estimateddistortion field to generate a matched filter for use in forming a teststatistics; means for comparing the test data with the reference data,taking into account the estimated distortion; means responsive to thecomparing means for making an identity-verification decision; andnonvolatile memory means for holding instructions for automaticoperation of the foregoing means.
 14. Apparatus for verifying theidentity of a person by comparing test data representing atwo-dimensional test image of that person's skin-pattern print withreference data derived from a two-dimensional reference skin-patternprint image obtained during a prior enrollment procedure; said apparatusbeing for use in the presence of an assumed distortion of the test imagerelative to the reference image; and said apparatus comprising:means forestimating the assumed distortion of the test image relative to areference image; means for comparing the test data with the referencedata, taking into account the estimated distortion; means responsive tothe comparing means for making an identity-verification decision; andwherein: the estimating means comprise means for using amaximum-likelihood method to estimate the distortion field; and saidusing means comprise means for taking account of a priori statistics inestimating the distortion field; and further comprising nonvolatilememory means for holding instructions for automatic operation of theforegoing means.
 15. The apparatus of claim 14, wherein:said using meanscomprise means for using a Fourier-space model for taking account of thea priori statistics.
 16. Apparatus for verifying the identity of aperson by comparing test data representing a two-dimensional test imageof that person's skin-pattern print with reference data derived from atwo-dimensional reference skin-pattern print image obtained during aprior enrollment procedure; said apparatus being for use in the presenceof an assumed distortion of the test image relative to the referenceimage; and said apparatus comprising:means for estimating the assumeddistortion of the test image relative to a reference image; means forcomparing the test data with the reference data, taking into account theestimated distortion; means responsive to the comparing means for makingan identity-verification decision; and wherein the estimating meanscomprise:means for demodulating the test data preliminary to extractinga distortion field therefrom, and means for applying informationdeveloped from the reference data as a carrier field, in demodulatingthe test data; and further comprising nonvolatile memory means forholding instructions for automatic operation of the foregoing means. 17.Apparatus for verifying the identity of a person by comparing test datarepresenting a two-dimensional test image of that person's skin-patternprint with reference data derived from a two-dimensional referenceskin-pattern print image obtained during a prior enrollment procedure;said apparatus being for use in the presence of an assumed distortion ofthe test image relative to the reference image; and said apparatuscomprising:means for estimating the assumed distortion of the test imagerelative to a reference image; wherein the estimating meanscomprise:means for avoiding errors due to phase shifts greater than halfthe local periodicity of an assumed carrier field, and means forbeginning the estimating with a first approximation that is localizedand of small magnitude, and iterating so that progressive approximationspropagate in the frequency or spatial domain, or both; and the avoidingmeans comprise means for controlling rate of propagation to minimizelikelihood of introducing a phase shift greater than half the localperiodicity in any single iteration; and further comprising: means forcomparing the test data with the reference data, taking into account theestimated distortion; means responsive to the comparing means for makingan identity-verification decision; and nonvolatile memory means forholding instructions for automatic operation of the foregoing means. 18.The apparatus of claim 17, wherein the controlling means comprise:meansfor monitoring a measure of the rate at which the distortion ischanging; and means, responsive to the monitoring means, for limitingthe rate of propagation as a function of position, in accordance withsaid measure.
 19. Apparatus for verifying the identity of a person bycomparing test data representing a two-dimensional test image of thatperson's skin-pattern print with reference data derived from atwo-dimensional reference skin-pattern print image obtained during aprior enrollment procedure; said apparatus being for use in the presenceof an assumed distortion of the test image relative to the referenceimage; and said apparatus comprising:means for estimating the assumeddistortion of the test image relative to a reference image; wherein theestimating means comprise means for downsampling the test data accordingto anticipated degree of abruptness of at least one type of distortion,in preparation for estimating the distortion; means for comparing thetest data with the reference data, taking into account the estimateddistortion; means responsive to the comparing means for making anidentity-verification decision; means for extracting from priorstatistics an estimate of the power spectral density for distortionfields generally; means for setting sampling intervals as a function ofposition, in accordance with the estimate of power spectral density; andnonvolatile memory means for holding instructions for automaticoperation of the foregoing means.
 20. A secured system subject to accesscontrol based upon surface-relief data from a relieved surface such as afinger; said system being for use in the presence of an assumeddistortion of the relieved surface; and said systemcomprising:utilization means, susceptible to misuse in the absence of aparticular such relieved surface that is related to an authorized user,said utilization means being selected from the group consisting of:afacility, apparatus, means for providing a financial service, and meansfor providing or receiving information; sensor means for acquiringsurface-relief data from such a relieved surface; means for processingthe data to determine identity of the relieved surface, and for applyingthe determined identity to control access to the utilization means, saidprocessing and applying means including:means for expressing the testdata in the form of local sinusoids; means for expressing referencedata, related to said particular relieved surface related to theauthorized user, in the form of local sinusoids; means for analyzing thedata to estimate the assumed distortion, means for comparing portions ofthe sinusoidally expressed test data with the sinusoidally expressedreference data related to said particular relieved surface related tothe authorized user, taking into account the estimated distortion, andmeans, responsive to the comparing means, for making anidentity-verification decision; and nonvolatile memory means for holdinginstructions for automatic operation of the foregoing means. 21.Apparatus for verifying the identity of a person by comparing test datarepresenting a two-dimensional test image of that person's skin-patternprint with reference data derived from a two-dimensional referenceskin-pattern print image obtained during a prior enrollment procedure;said apparatus being for use in the presence of an assumed distortion ofthe test image relative to the reference image; and said apparatuscomprising:means for estimating the assumed distortion of the test imagerelative to a reference image; means for comparing the test data withthe reference data, taking into account the estimated distortion; meansfor extracting from the test data an estimate of noise variance in thetest data as a function of position in the test image; wherein theestimating means or the comparing means, or both, comprise means forweighting the importance of the estimating or comparing, or both, as afunction of position in accordance with the noise-variance estimate forthe corresponding position; means responsive to the comparing means formaking an identity-verification decision; and nonvolatile memory meansfor holding instructions for automatic operation of the foregoing means.22. Apparatus for verifying the identity of a person by comparing testdata representing a two-dimensional test image of that person'sskin-pattern print with reference data derived from a two-dimensionalreference skin-pattern print image obtained during a prior enrollmentprocedure; said apparatus being for use in the presence of an assumeddistortion of the test image relative to the reference image; and saidapparatus comprising:means for estimating the assumed distortion of thetest image relative to a reference image; wherein said estimating meanscomprise means for using a maximum-likelihood method to estimate thedistortion field and thereby generate a matched filter for use informing a test statistic; means for comparing the reference data withthe test data, using the test statistic; means responsive to thecomparing means for making an identity-verification decision; andnonvolatile memory means for holding instructions for automaticoperation of the foregoing means.
 23. Apparatus for verifying theidentity of a person by comparing test data representing atwo-dimensional test image of that person's skin-pattern print withreference data derived from a two-dimensional reference skin-patternprint image obtained during a prior enrollment procedure; said apparatusbeing for use in the presence of an assumed distortion of the test imagerelative to the reference image; and said apparatus comprising:means forusing a maximum-likelihood method that takes account of a prioristatistics, to estimate the assumed distortion of the test imagerelative to a reference image; means for comparing the test data withthe reference data, taking into account the estimated distortion; meansresponsive to the comparing means for making an identity-verificationdecision; and nonvolatile memory means for holding instructions forautomatic operation of the foregoing means.
 24. Apparatus for verifyingthe identity of a person by comparing test data representing atwo-dimensional test image of that person's skin-pattern print withreference data derived from a two-dimensional reference skin-patternprint image obtained during a prior enrollment procedure; said apparatusbeing for use in the presence of an assumed distortion of the test imagerelative to the reference image; and said apparatus comprising:means forapplying information developed from the reference data as a carrierfield, to demodulate the test data; means for estimating the assumeddistortion of the demodulated test image relative to a reference image;means for comparing the test data with the reference data, taking intoaccount the estimated distortion; means responsive to the comparingmeans for making an identity-verification decision; and furthercomprising nonvolatile memory means for holding instructions forautomatic operation of the foregoing means.
 25. Apparatus for verifyingthe identity of a person by comparing test data representing atwo-dimensional test image of that person's skin-pattern print withreference data derived from a two-dimensional reference skin-patternprint image obtained during a prior enrollment procedure; said apparatusbeing for use in the presence of an assumed distortion of the test imagerelative to the reference image, said assumed distortion beingsuperimposed on an assumed carrier field; and said apparatuscomprising:means for estimating the assumed distortion of the test imagerelative to a reference image; means for estimating or establishing theassumed carrier field; means for detecting phase discontinuities orreversals in the skin-pattern print image, to avoid skin-pattern phaseshift greater than half the local periodicity of the assumed carrierfield; means for comparing the test data with the reference data, takinginto account the estimated distortion substantially free of effects ofsuch skin-pattern phase shift greater than half the local periodicity ofthe assumed carrier field; means responsive to the comparing means formaking an identity-verification decision; and nonvolatile memory meansfor holding instructions for automatic operation of the foregoing means.26. Apparatus for verifying the identity of a person by comparing testdata representing a two-dimensional test image of that person'sskin-pattern print with reference data derived from a two-dimensionalreference skin-pattern print image obtained during a prior enrollmentprocedure; said apparatus being for use in the presence of an assumeddistortion of the test image relative to the reference image; and saidapparatus comprising:means for establishing a first approximation of theassumed distortion, said first approximation being localized and ofsmall magnitude; means for establishing further approximationsiteratively so that progressive approximations propagate in thefrequency or spatial domain, or both, to thereby estimate the overalldistortion of the test image relative to a reference image; means forcontrolling rate of propagation to minimize likelihood of introducing,in any single iteration, a phase shift greater than half the localperiodicity of an assumed carrier field; and further comprising: meansfor comparing the test data with the reference data, taking into accountthe estimated distortion; means responsive to the comparing means formaking an identity-verification decision; and nonvolatile memory meansfor holding instructions for automatic operation of the foregoing means.27. Apparatus for verifying the identity of a person by comparing testdata representing a two-dimensional test image of that person'sskin-pattern print with reference data derived from a two-dimensionalreference skin-pattern print image obtained during a prior enrollmentprocedure; said apparatus being for use in the presence of an assumeddistortion of the test image relative to the reference image; and saidapparatus comprising:means for estimating power spectral density ofskin-pattern print data; means for downsampling the test data accordingto anticipated degree of abruptness of at least one type of distortion;means for employing the estimated power spectral density in estimatingthe assumed distortion of the downsampled test image relative to areference image; means for comparing the test data with the referencedata, taking into account the thereby-estimated distortion; meansresponsive to the comparing means for making an identity-verificationdecision; and nonvolatile memory means for holding instructions forautomatic operation of the foregoing means.